student: instructor: alfredo alvarez coursealvarezmathhelp.com/math1414alvarez99.pdf · 5. 6. state...

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Student: _____________________Date: _____________________

Instructor: Alfredo AlvarezCourse: PreCalculus Sullivan 10e

Assignment: math1414alvarez99

For the given equation, list the intercepts and test for symmetry.

y = x − x − 62

What are the intercept(s)? Select the correct choice below and fill in any answer boxes within your choice.

A.

(Type an ordered pair. Use a comma to separate answers as needed.)

B. There are no intercepts.

Is the graph of the equation symmetric with respect to the x-axis?

Yes

No

Is the graph of the equation symmetric with respect to the y-axis?

Yes

No

Is the graph of the equation symmetric with respect to the origin?

Yes

No

For the given equation, list the intercepts and test for symmetry.

y =2x

x2 + 49

What are the intercept(s)? Select the correct choice below and fill in any answer boxes within your choice.

A. .



Is the graph of the equation symmetric with respect to the x-axis?

Yes

No

Is the graph of the equation symmetric with respect to the y-axis?

Yes

No

Is the graph of the equation symmetric with respect to the origin?

Yes

No

The intercept(s) is/are

math1414alvarez99 https://xlitemprod.pearsoncmg.com/api/v1/print/math

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3.

4.

Graph the line that contains the point P and has slope m. Find the point-slope form of the equation of the line.

P ; m= (8,4) = 4

Use the graphing tool to graph the line. Use the given point when drawing the line.

The point-slope form of the equation of the line is

.

(Use integers or fractions for any numbers in the equation.)

For the equation , do the following.x + y − 4x − 2y − 20 = 02 2

(a) Find the center (h,k) and radius r of the circle.(b) Graph the circle.(c) Find the intercepts, if any.

(a) The center is .

(Type an ordered pair.)

The radius is r .=

(b) Use the graphing tool to graph the circle.

(c) Find the intercepts, if any. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A. The intercept(s) is/are.

(Type an ordered pair. Use a comma to separate answers as needed. Type exact answers for each coordinate, using radicals as needed.)

B. There is no intercept.


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5.

6.

State the domain and range for the following relation. Then determine whether the relation represents a function.

Beni

Geby

Saul

Makin

BudRosa

Zena

Abby Hattie

Brother Sister

Choose the correct answer below.

Domain : { }Hattie, Bud, RosaRange : { }Abby, Beni, Geby

Domain : { }Hattie, Bud, Rosa, ZenaRange : { }Abby, Beni, Geby, Saul, Makin

Domain : { }Abby, Beni, Geby, Saul, MakinRange : { }Hattie, Bud, Rosa, Zena

Domain : { }Saul, MakinRange : { }Zena

Does the relation represent a function?

A. No, because each element in the first set does not correspond to exactly one element in the second set.

B. No, because an element in the second set corresponds to multiple elements in the first set.

C. Yes, because each element in the first set corresponds to exactly one element in the second set.

D. Yes, because each element in the second set corresponds to exactly one element in the first set.


{ }( )3,5 , ( )− 9,5 , ( )7,6 , ( )3,12

The domain of the relation is .(Use a comma to separate answers as needed.)

The range of the relation is .(Use a comma to separate answers as needed.)

Does the relation represent a function? Choose the correct answer below.

A.

B. The relation is not a function because there are ordered pairs with as the first element and different second elements.

3

C. The relation is a function because there are no ordered pairs with the same first element and different second elements.

D. The relation is not a function because there are ordered pairs with as the second element and different first elements.

6

The relation is a function because there are no ordered pairs with the same second element and different first elements.


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7.

8.


{ }( − 3,4), ( − 2,1), ( − 1,0), (0,1)

The domain of the relation is .(Use a comma to separate answers as needed.)

The range of the relation is .(Use a comma to separate answers as needed.)

Does the relation represent a function? Choose the correct answer below.

A. The relation is a function because there are no ordered pairs with the same first element and different second elements.

B. The relation is not a function because there are ordered pairs with as the first element and different second elements.

− 3

C. The relation is a function because there are no ordered pairs with the same second element and different first elements.

D. The relation is not a function because there are ordered pairs with as the second element and different first elements.

0

Find the following for the function .f(x) = 3x + 4x − 32

(a) f(0) (b) f(4) (c) f( − 4) (d) f( − x)(e) − f(x) (f) f(x )+ 1 (g) f( x)4 (h) f(x + h)

(a) f(0) (Simplify your answer.)=

(b) f( ) (Simplify your answer.)4 =

(c) (Simplify your answer.)f( − 4) =

(d) (Simplify your answer.)f( − x) =

(e) (Simplify your answer.)− f(x) =

(f) f(x ) (Simplify your answer.)+ 1 =

(g) f( x) (Simplify your answer.)4 =

(h) (Simplify your answer.)f(x + h) =


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9.

10.

11.

12.

Find the following for the function f(x) = .6x + 7

9x − 8

(a) f(0) (b) f(1) (c) f( 1)− (d) f( x)−(e) f(x)− (f) f(x )+ 2 (g) f( x)5 (h) f(x h)+

(a) f(0) =

(Simplify your answer. Type an integer or a simplified fraction.)

(b) f(1) =


(c) f( 1)− =


(d) f( x)− =

(Simplify your answer. Use integers or fractions for any numbers in the expression.)

(e) f(x)− =


(f) f(x )+ 2 =


(g) f( x)5 =


(h) f(x h)+ =


Find the domain of the function.

g(x) =x + 4

x2 − 25

The domain is .

(Type your answer in interval notation.)

Find the domain of the given function.

F(x) = x − 6

x3 + 6x

The domain of F is . (Type your answer in interval notation.)


f(x) = 5x − 40

The domain is . (Type your answer in interval notation.)


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13.

14.


p(x) =5

x + 4

In set notation, the domain of the function is . (Type an inequality.)x


f(x) =4

x − 5

The domain is .

(Type your answer in interval notation. )


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15. For the given functions f and g, complete parts (a)-(h). For parts (a)-(d), also find the domain.

;f(x) = 2x + 3 g(x) = 7x − 2

(a) Find (f g)(x).+

(f g)(x) (Simplify your answer.)+ =

What is the domain of f g? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

+

A. The domain is .x(Use

B. The domain is .{ }x x is any real number

(b) Find .(f − g)(x)

(Simplify your answer.)(f − g)(x) =

What is the domain of ? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

f − g



(c) Find (f g)(x).•

(f g)(x) (Simplify your answer.)• =

What is the domain of f g? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

•



(d) Find .(x)f

g

(Simplify your answer.)(x)f

g=

What is the domain of ? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.f

g



(e) Find (f g)( ).+ 2

integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)





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16.

17.

(f g)( ) (Type an integer or a simplified fraction.)+ 2 =

(f) Find (f g)( ).− 3

(f g)( ) (Type an integer or a simplified fraction.)− 3 =

(g) Find (f g)( ).• 4

(f g)( ) (Type an integer or a simplified fraction.)• 4 =

(h) Find .(1)f

g

(Type an integer or a simplified fraction.)(1)f

g=

Find the difference quotient of f; that is, find for the following function. Be sure to simplify.,f(x + h) − f(x)

hh ≠ 0,

f(x) = x − 4x + 62

=f(x + h) − f(x)

h

Given f(x) = x x , find the value(s) for x such that f(x) .2 − 3 + 2 = 30

The solution set is .


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18.


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Use the graph of the function f shown to the right to answer parts (a)-(n).

(a) Find f( ) and f( ).− 21 − 6

f( − 21) =

f( − 6) =

(b) Find f( ) and f( ).18 0

f(18) =

f(0) =

(c) Is f( ) positive or negative?6

Negative

Positive

(d) Is f( ) positive or negative?− 9

Positive

Negative

(e) For what value(s) of x is f(x) 0?=

x =

(Use a comma to separate answers as needed.)

(f) For what values of x is f(x) 0?>

(Type a compound inequality. Use a comma to separate answers as needed.)

(g) What is the domain of f?

The domain of f is .x(Type a compound inequality.)

(h) What is the range of f?

The range of f is .y(Type a compound inequality.)

(i) What are the x-intercept(s)?

x =

(Type an integer or a simplified fraction. Use a comma to separate answers as needed.)

(j) What are the y-intercept(s)?

y =

(Type an integer or a simplified fraction. Use a comma to separate answers as needed.)

(k) How often does the line y 1 intersect the graph?=

time(s)

−6−12−18 18126

(−21,−2)

(−18,0)

(−9,3)

(−6,2)(−3,0)

(0,−1)

(6,−2)

(12,0)

(18,2)

−2

2

−4

4


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19.

20.

21.

The graph of two functions, f and g, is illustrated below. Use the graph to answer parts (a) through (f).

(a) (f + g)(2) =

(Simplify your answer.)

(b) (f + g)(4) =


(c) (f − g)(6) =


(d) (g − f)(6) =


(e) (f • g)(2) =


(f) (4)f

g=


Use the graph of the function f given below to answer the question.

Is f strictly on the interval increasing ( − 8, − 5)?

No

Yes

List the intervals on which f is decreasing.

(Type your answer in interval notation. Use a comma to separate answers as needed.)


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22.

23.

24.

Use the graph of the function f given below to answer the questions.

Is there a local at maximum x = − 2?

Yes

No

If there is a local at x , what is it? Select the correct choice below and fill in any answer boxes within your choice.

maximum = − 2

A. The local is

y .

maximum

=

(Type an integer.)

B. There is no local at x .maximum = − 2

Use the graph of the function f given below to answer the questions.

List the values of x at which f has a local Select the correct choice below and fill in any answer boxes within your choice.

minimum.

A. x =

(Type an integer. Use a comma to separate answers as needed.)

B. There are no local .minima

What are these local , if they exist? Select the correct choice below and fill in any answer boxes within your choice.

minima

A. The local are .minima


B. There are no local .minima

Find the absolute of f on [ , ].maximum − 8 9

Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.

A.

f = .

B. There is no absolute .maximum

The absolute of f is maximum

(Type integers or fractions.)


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25.

Use the graph to find:

(a) The numbers, if any, at which f has a local maximum. What are these local maxima?(b) The numbers, if any, at which f has a local minimum. What are these local minima?

(a) Select the correct choice below and fill in any answer boxes within your choice.

A. The value(s) of x at which f has a local

maximum is/are x .=


B. There are no values of x at which f has a local maximum.

Select the correct choice below and fill in any answer boxes within your choice.

A. The local maxima is/are

y .=


B. There are no local maxima.

(b) Select the correct choice below and fill in any answer boxes within your choice.

A. The value(s) of x at which f has a local

minimum is/are x .=


B.


A. The local minima is/are

y .=


B. There are no local minima.

There are no values of x at which f has a local minimum.


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26.

27.

Using the given graph of the function f, find the following.

(a) The numbers, if any, at which f has a local maximum. What are these local maxima?(b) The numbers, if any, at which f has a local minimum. What are these local minima?

(a) Find the value(s) of x at which f has a local maximum. Select the correct choice below and fill in any answer boxes in your choice.

A. x =

(Type an exact answer, using as needed. Use a comma to separate answers as needed.)

B. There is no solution.

Find the local maximum. Select the correct choice below and fill in any answer boxes in your choice.

A.



(b) Find the value(s) of x at which f has a local minimum. Select the correct choice below and fill in any answer boxes in your choice.

A.



Find the local minimum. Select the correct choice below and fill in any answer boxes in your choice.

A.



Determine algebraically whether the given function is even, odd, or neither.

f(x) = − 7x + 6x4 2

Even

Odd

Neither

x =


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28.

29.

30.

31.

Determine algebraically whether the given function is even, odd, or neither.

g(x) = 3x − 62

Odd

Neither

Even

Find the average rate of change of f(x) := − 2x + 12

(a) From to 4 6(b) From to − 2 0(c) From to 0 3

(a) From to 4 6

(b) From to − 2 0

(c) From to 0 3

Let h(x) .= x − 8x2

(a) Find the average rate of change from to .4 9(b) Find an equation of the secant line containing and (4, h(4)) (9, h(9)).

(a) The average rate of change from to is . (Simplify your answer.)4 9

(b) An equation of the secant line containing and is (4, h(4)) (9, h(9)) .(Type your answer in slope-intercept form.)

g(x) = − x + 27x3

(a) Determine whether g is even, odd, or neither. (b) There is a local minimum of at . Determine the local maximum.− 54 − 3

(a) Determine whether g is even, odd, or neither.

Odd

Neither

Even

(b) There is a local minimum of at . Determine the local maximum.− 54 − 3

The local maximum is . (Type an integer or a decimal.)


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32.

33.

34.

Which of the following functions has a graph that is symmetric about the y-axis?

Select all that apply.

A. y x= 3

B. y = x

C. y = x

D. y =1

x

Match the graph given to the right to its function.


Square root function Cube root function

Square function Identity function

Absolute value function Constant function

Cube function Reciprocal function

Match the graph given to the right to its function.


Identity function Constant function

Absolute value function Square function

Cube root function Reciprocal function

Square root function Cube function


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35. Sketch the graph of the function. Be sure to label three points on the graph.

f(x) =6

x

Choose the correct graph below.

A. B. C.


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36. The function f is defined as follows.

f(x) =− 3x + 4

3x − 2

if x < 1

if x ≥ 1

(a) Find the domain of the function.(b) Locate any intercepts.(c) Graph the function.(d) Based on the graph, find the range.(e) Is f continuous on its domain?

(a) The domain of the function f is .


(b) Locate any intercepts. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A. The intercept(s) is/are .



(c) Choose the correct graph below.

A. B. C. D.

(d) The range of the function f is .


(e) Is f continuous on its domain? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A. Yes, f is continuous on its domain.

B. No, f is discontinuous at x .=



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37.

38.

The function f is defined as follows.

f(x) =4 + x

x2

if x < 0

if x ≥ 0

(a) Find the domain of the function.(b) Locate any intercepts.(c) Graph the function.(d) Based on the graph, find the range.(e) Is f continuous on its domain?

(a) The domain of the function f is .


(b) Locate any intercepts. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A. The intercept(s) is/are .



(c) Choose the correct graph of f(x) below.

A. B. C. D.

(d) The range of the function f is .


(e) Is f continuous on its domain? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A. No, f is discontinuous at x .=


B. Yes, f is continuous on its domain.

Starting with the graph of a basic function, graph the following function using the techniques of shifting,compressing, stretching, and/or reflecting. Find the domain and range of the function.

g(x) = x − 33

Use the graphing tool to graph the equation.

The domain of g(x) is .


The range of g(x) is .



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39. Graph the following function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function shown to the right. Find the domain and range of the function.

h(x) = x + 2


A. B. C. D.

Find the domain of h(x).


Find the range of h(x).



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40. The relationship between the Celsius (°C) and Fahrenheit (°F) scales for measuring temperature is given by the equation

F The relationship between the Celsius (°C) and Kelvin (K) scales is K C 273. Graph the equation

F using degrees Fahrenheit on the y-axis and degrees Celsius on the x-axis. Use transformations to obtain the

graph showing the relationship between Kelvin and Fahrenheit temperatures.

= C + 329

5= +

= C + 329

5

Graph the equation F using degrees Fahrenheit on the y-axis and degrees Celsius on the x-axis. Choose the

correct graph below.

= C + 329

5

A. B. C. D.

Using transformations obtain the graph that shows the relationship between Kelvin and Fahrenheit temperatures. Choose the correct graph below.

A. B. C. D.


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41. For the data given below, answer parts (a) through (d).

x − 4 − 2 0 2 4y − 5 0 1 4 5

(a) Find the equation of the line containing the first and the last data points.

y =

(Type your answer in slope-intercept form. Use integers or fractions for any numbers in the expression.)

(b) Draw a scatter diagram and the line found in part (a) on the same axes.


A. B. C. D.

(c) Use a graphing utility to find the line of best fit.

Which of the following is the equation of the line of best fit?

A. y = 1.2x − 1

B. y = − 1.2x + 1

C. y = 1.2x + 1

D. y = − 1.2x − 1

(d) Use a graphing utility to draw the scatter diagram and graph the line of best fit on it.

Choose the correct graph below. The viewing window for each graph is .[ − 8,8,2] by [ − 10,10,2]

A. B. C. D.


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42.

43.

For the data given below, answer parts (a) through (d).

x − 22 − 19 − 17 − 16 − 12y 99 119 117 129 139

(a) Find the equation of the line containing the first and the last data points.

y =

(Type your answer in slope-intercept form. Use integers or fractions for any numbers in the expression.)

(b) Draw a scatter diagram and the line found in part (a) on the same axes.


A. B. C. D.

(c) Use a graphing utility to find the line of best fit.

Which of the following is the equation of the line of best fit?

A. y = − 3.8613x + 187.0146

B. y = 3.9613x + 187.0146

C. y = 3.8613x + 187.0146

D. y = − 3.9613x + 187.0146

(d) Use a graphing utility to draw the scatter diagram and graph the line of best fit on it.


A. B. C. D.

[ 25,0,5] by [90, ,10]− 207

Match the function to one of the given graphs.f(x) = x − 2x + 32


A. B. C. D.


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44.

45.

Graph the function by starting with the

graph of and using transformations (shifting,stretching/compressing, and/or reflecting).

f(x) = (x + 5) − 32

y = x2

Use the graphing tool to graph the function.

Complete parts (a)-(d) for the functions and .f(x) = 2x − 1 g(x) = x − 92

(a) Graph f and g on the same Cartesian plane. Choose the correct graph below.

A. B. C. D.

(b) Solve f(x) = g(x).

The solution set is .(Use a comma to separate answers as needed.)

(c) Use the result of part (b) to label the points of intersection of the graphs of f and g.

The points of intersection are .


(d) Shade the region for which that is, the region below f and above g. Choose the correct graph below.f(x) > g(x),

A. B. C. D.

E. F. G. H.


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46.

47.

48.

Farmer Ed has meters of fencing,and wants to enclose a rectangular plot that borders on a river. If Farmer Ed does not fence the side along the river,what is the largest area that can beenclosed?

6,000

x x

The largest area that can be enclosed is square meters.

A projectile is fired from a cliff feet above the water at an inclination of 45° to the horizontal, with a muzzle velocity of feet per second. The height h of the projectile above the water is given by

22055

h(x) = + x + 220− 32x2

(55)2

where x is the horizontal distance of the projectile from the face of the cliff. Use this information to answer the following.

(a) At what horizontal distance from the face of the cliff is the height of the projectile a maximum?

x feet=


(b) Find the maximum height of the projectile.

h feet=


(c) At what horizontal distance from the face of the cliff will the projectile strike the water?

x feet=

(Round to the nearest foot as needed.)

(d) Using a graphing utility, graph the function h, Which of the following shows the graph of h(x)?0 ≤ x ≤ 210.In all graphs, the window is by [0, 210] [0, 260], Xscl = 20, Yscl = 50.

A. B. C. D.

(e) When the height of the projectile is 100 feet above the water, how far is it from the cliff?

x feet=

(Round to the nearest foot as needed.)

Solve the following inequality.

x + 9x + 14 < 02

Select the correct choice below and, if necessary, fill in the answer box.

A. The solution set is .

(Type your answer in interval notation. Use integers or fractions for any numbers in theexpression.)

B. There is no real solution.

6,000 −2x


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49.

50.

51.

52.


x − 4x > 02






x + 4x > 122





What is the domain of the function ?f(x) = x2 − 64

The domain is . (Type your answer in interval notation.)

Determine whether the following function is a polynomial function. If the function is a polynomial function, state its degree. If it is not, tell why not. Write the polynomial in standard form. Then identify the leading term and the constant term.

G(x) = 4(x − 1)2 x2 + 3

Determine whether G(x) is a polynomial or not. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A. .

(Type an integer or a fraction.)

B. It is not a polynomial because the variable x is raised to the power, which is

not a nonnegative integer.(Type an integer or a fraction.)

C. It is not a polynomial because the function is the ratio of two distinct polynomials, and the polynomial in the denominator is of positive degree.

Write the polynomial in standard form. Then identify the leading term and the constant term. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A. The polynomial in standard form is G(x) with leading term

and constant .

=

(Simplify your answers. Use integers or fractions for any numbers in the expressions.)

B. The function is not a polynomial.

It is a polynomial of degree


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53.

54.

55.

56.

Form a polynomial whose zeros and degree are given.

Zeros: , , ; degree: 3− 3 3 9

Type a polynomial with integer coefficients and a leading coefficient of 1 in the box below.

f(x) (Simplify your answer.)=

Form a polynomial whose real zeros and degree are given.

Zeros: , 0, ; degree: 3− 3 5

Type a polynomial with integer coefficients and a leading coefficient of 1.

f(x) (Simplify your answer.)=

Find a polynomial function with the zeros , , whose graph passes through the point .− 2 3 5 ( )7,144

f(x) =


(1) crosses

touches

(2) crosses

touches

For the polynomial function below: (a) List each real zero and its multiplicity. (b) Determine whether the graph crosses or touches the x-axis at each x-intercept. (c) Determine the maximum number of turning points on the graph. (d) Determine the end behavior; that is, find the power function that the graph of f resembles for large values of .x

f(x) ( )= − 8 x − 5 (x + 7)2

(a) Find any real zeros of f. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A. The real zero(s) of f is/are .

(Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)

B. There are no real zeros.

The multiplicity of the larger zero is .

(Type a whole number.)

The multiplicity of the smaller zero is .


(b) The graph (1) the x-axis at the larger x-intercept.

The graph (2) the x-axis at the smaller x-intercept.

(c) The maximum number of turning points on the graph is .


(d) Type the power function that the graph of f resembles for large values of .x

y =


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57.

(1) crosses

touches

(2) crosses

touches

(3) crosses

touches

Analyze the polynomial function f(x) . Answer parts (a) through (e). [Hint: First factor the polynomial.]= 4x − x3

(a) Determine the end behavior of the graph of the function.

The graph of f behaves like y for large values of .= x

(b) Find the x- and y-intercepts of the graph of the function.

The x-intercept(s) is/are .

(Type an integer or a simplified fraction. Use a comma to separate answers as needed. Type each answer only once.)

The y-intercept is .

(Type an integer or a simplified fraction.)

(c) Determine the zeros of the function and their multiplicity. Use this information to determine whether the graph crosses or touches the x-axis at each x-intercept.

The zero(s) of f is/are .

(Type an integer or a simplified fraction. Use a comma to separate answers as needed. Type each answer only once.)

The smallest zero is a zero of multiplicity , so the graph of f (1) the x-axis at

x . The middle zero is a zero of multiplicity , so the graph of f (2) the

x-axis at x . The largest zero is a zero of multiplicity , so the graph of f

(3) the x-axis at x .

=

=

=

(d) Determine the maximum number of turning points on the graph of the function.

The graph of the function will have at most turning points.

(e) Use the information in parts (a) through (d) to draw a complete graph of the function. Choose the correct graph below.

A. B. C. D.


28 of 60 10/6/2017, 3:29 PM

58.

59.

60.

Construct a polynomial function f with the following characteristics.

zeros: (multiplicity ), (multiplicity ), and (multiplicity )− 3 1 1 1 4 2degree 4contains the point ( , )3 − 24


A. f(x) = 2(x + 3)(x − 1)(x − 4)2

B. f(x) = − 2(x + 3)(x − 1)(x − 4)2

C. f(x) = 2(x + 3)(x − 1) (x − 4)2 2

D. f(x) = − 2(x + 3)(x − 1)(x − 4)

Find the domain of the following rational function.

R(x) =11x

x + 9

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A. The domain of R(x) is {x | }.

(Type an inequality. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)

B. The domain of R(x) is the set of all real numbers.

Find the domain of the following rational function.

H(x) =− 4x2

(x − 4)(x + 3)


A.

(Type an inequality. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)

B. The domain of H(x) is the set of all real numbers.

The domain of H(x) is {x | }.


29 of 60 10/6/2017, 3:29 PM

61.

62.

Find the vertical, horizontal, and oblique asymptotes, if any, for the following rational function.

R(x) =18x

x + 15


A. The vertical asymptote(s) is/are x .=


B. There is no vertical asymptote.


A. The horizontal asymptote(s) is/are y .=


B. There is no horizontal asymptote.


A.


B. There is no oblique asymptote.

Find the vertical, horizontal, and oblique asymptotes, if any, for the given rational function.

Q(x) =5x2 − 13x − 6

2x2 − 3x − 9


A. The vertical asymptote(s) is/are x .=

(Use a comma to separate answers as needed. Use integers or fractions for any numbers in the expression.)



A. The horizontal asymptote(s) is/are y .=




A. The oblique asymptote(s) is/are y .=



The oblique asymptote(s) is/are y .=


30 of 60 10/6/2017, 3:29 PM

63.

64.

65.

Find the vertical, horizontal, and oblique asymptotes, if any, for the given rational function.

R(x) =10x2 + 27x − 28

2x + 7


A. The vertical asymptote(s) is/are x = .(Usethe



A. The horizontal asymptote(s) is/are y = .(Usethe



A. The oblique asymptote(s) is/are y = .(Usethe


Solve the inequality algebraically.

> 0x + 8

x − 3

The solution is .

(Simplify your answer. Type your answer in interval notation. Use integers or fractions for any numbers in the expression.)

Solve the inequality algebraically.

≤ 1x + 13

x − 14

The solution is .

(Simplify your answer. Type your answer in interval notation. Use integers or fractions for any numbers in the expression.)

a comma to separate answers as needed. Use integers or fractions for any numbers in expression.)




31 of 60 10/6/2017, 3:29 PM

66.

67.

68.

List the potential rational zeros of the polynomial function. Do not attempt to find the zeros.

f(x) = 55x − x + 1214 2

Choose the answer below that lists the potential rational zeros.

A.− 1,1, − 11,11, − 121,121, − , , − , , − ,

1

11

1

11

1

5

1

5

1

55

1

55

B.− 1,1, − 11,11, − 121,121, − , , − , , − , , − , , − ,

1

11

1

11

1

5

1

5

1

55

1

55

5

11

5

11

5

121

5

121

C.− 1,1, − 11,11, − 121,121, − , , − , , − , , − , , − ,

1

11

1

11

1

5

1

5

1

55

1

55

11

5

11

5

121

5

121

5

D.− 1,1, − 11,11, − 5,5, − 55,55, − , , − , , − , , − , , − ,

1

11

1

11

1

5

1

5

1

55

1

55

5

11

5

11

5

121

5

121

Use the rational zeros theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers.

f(x) = x + 3x − 13x − 153 2

Find the real zeros of f. Select the correct choice below and, if necessary, fill in the answer box to complete your answer.

A. x =

(Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions for any rational numbers in the expression. Use a comma to separate answers asneeded.)


Use the real zeros to factor f.

f(x) =

(Simplify your answer. Type your answer in factored form. Type an exact answer, using radicals as needed. Use integers or fractions for any rational numbers in the expression.)

Use the rational zeros theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers.

f(x) = x + 4x − 9x − 16x + 204 3 2

What are the real zeros? Select the correct choice below and, if necessary, fill in the answer box to complete your answer.

A.

(Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions for any rational numbers in the expression. Use a comma to separate answers asneeded.)


Use the real zeros to factor f.

f(x) =

(Simplify your answer. Type your answer in factored form. Type an exact answer, using radicals as needed. Use integers or fractions for any rational numbers in the expression.)

x =


32 of 60 10/6/2017, 3:29 PM

69.

70.

71.

Find bounds on the real zeros of the polynomial function.

f(x) = x − 3x − 44 2

The lower bound is and the upper bound is .

(Type integers or simplified fractions.)

Use the Intermediate Value Theorem to show that the polynomial function has a zero in the given interval.

; f(x) = 14x − 6x + 7x − 14 2 [ ]0, 3

Enter the value of f(0).

(Simplify.)f(0) =

Enter the value of f(3).

(Simplify.)f(3) =

According to the Intermediate Value Theorem, does f have a zero in the given interval?

Yes

No

If f(x) and g(x) , then which of the following does (f g)(x) equal?= x + 4 =3

x


3

x + 4

+ 43

x

3

x + 4

3

x+ 4


33 of 60 10/6/2017, 3:29 PM

72.

73.

74.

75.

Evaluate each expression using the values given in the table.

x 3− 2− 1− 0 1 2 3 f(x) − 5 − 4 − 3 1− 3 4 5 g(x) 8 3 0 1− 0 3 8

a. (f g)( )1 b. (f g)( )− 1 c. (g f)( )− 1d.(g f)( )0 e. (g g)( )− 2 f. (f f)( )− 1

a. (f g)( )1 =

b. (f g)( )− 1 =

c. (g f)( )− 1 =

d. (g f)( )0 =

e. (g g)( )− 2 =

f. (f f)( )− 1 =

Given and find the following expressions.f(x) = 8x g(x) = 4x + 5,2

(a) (b) (c) (d) (f g)(4) (g f)(2) (f f)(1) (g g)(0)

(a) = (Simplify your answer.)(f g)(4)

(b) = (Simplify your answer.)(g f)(2)

(c) = (Simplify your answer.)(f f)(1)

(d) = (Simplify your answer.)(g g)(0)

For and find and Then determine whether f(x) = 6x − 5 g(x) = (x + 5),1

6(f g)(x) (g f)(x). (f g)(x) = (g f)(x).

What is ?(f g)(x)

= (f g)(x)

What is ?(g f)(x)

=(g f)(x)

Does = ?(f g)(x) (g f)(x)

Yes

No

For the following function, determine whether the function is one-to-one.

{(2,6), (3,9), ( − 8,3), (1, − 8)}

Is the function one-to-one?

Yes

No


34 of 60 10/6/2017, 3:29 PM

76.The graph of a function f is given. Use the horizontal-linetest to determine whether f is one-to-one.

Is f one-to-one? Choose the correct answer below.

No

Yes


35 of 60 10/6/2017, 3:29 PM

77.

The function is one-to-one.f(x) = x + 83

(a) Find the inverse of f and check the answer.

(b) Find the domain and the range of f and .f − 1

(c) Graph f, , and y x on the same coordinate axes.f − 1 =

(a) f (x)− 1 =


(b) Find the domain of f. Select the correct choice belowand, if necessary, fill in the answer box to complete your choice.

A. The domain is .x x ≤

B. The domain is .x x ≥

C. The domain is .x x ≠

D. The domain is the set of all real numbers.

Find the range of f. Select the correct choice below and, ifnecessary, fill in the answer box to complete your choice.

A. The range is .y y ≥

B. The range is .y y ≠

C. The range is .y y ≤

D. The range is the set of all real numbers.

Find the domain of . Select the correct choice belowand, if necessary, fill in the answer box to complete your choice.

f − 1

A. The domain is .x x ≥

B. The domain is .x x ≠

C. The domain is .x x ≤


Find the range of . Select the correct choice below and,if necessary, fill in the answer box to complete your choice.

f − 1



C. .


(c) Graph f, , and y x on the same coordinate axes. The graph of y x is shown using dashed line. Choose the correct graph below.

f − 1 ==

A. B.

C. D.

The range is y y ≤


36 of 60 10/6/2017, 3:29 PM

78.

The function is one-to-one.f(x) =1

x + 10(a) Find the inverse of f and check the answer.

(b) Find the domain and the range of f and .f − 1

(c) Graph f, , and y x on the same coordinate axes.f − 1 =

(a) f (x)− 1 =


(b) Find the domain of f. Select the correct choice belowand, if necessary, fill in the answer box to complete your choice.

A. The domain is .x x ≠

B. The domain is .x x ≤

C. The domain is .x x ≥


Find the range of f. Select the correct choice below and, ifnecessary, fill in the answer box to complete your choice.

A. The range is .y y ≠

B. The range is .y y ≥



Find the domain of . Select the correct choice belowand, if necessary, fill in the answer box to complete your choice.

f − 1

A. The domain is .x x ≤

B. The domain is .x x ≥

C. The domain is .x x ≠


Find the range of . Select the correct choice below and,if necessary, fill in the answer box to complete your choice.

f − 1





(c) Graph f, , and y x on the same coordinate axes. The graph of y x is shown using dashed line. Choose the correct graph below.

f − 1 ==

A. B.

C. D.


37 of 60 10/6/2017, 3:29 PM

79.

80.

81.

82.

Approximate each number using a calculator.

(a) 33.14 (b) 33.141 (c) 33.1415 (d) 3

(a) (Round to three decimal places as needed.)33.14

(b) (Round to three decimal places as needed.)33.141

(c) (Round to three decimal places as needed.)33.1415

(d) (Round to three decimal places as needed.)3

Solve the equation.

4 = 645x + 1

x =

(Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed.)

Solve the equation.

4 = 32− x + 28 x

The solution set is .(Type an integer or a simplified fraction. Use a comma to separate answers as needed.)

If a single pane of glass obliterates % of the light passing through it, then the percent p of the light that passes through nsuccessive panes is given approximately by the following function.

9

p(n) = 100(0.91)n

(a) What percent of light will pass through panes?15(b) What percent of light will pass through panes?35

(a) What percent of light will pass through panes?15

p(15) =% (Round to the nearest whole

number.)

(b) What percent of light will pass through panes?35

p(35) =% (Round to the nearest whole

number.)


38 of 60 10/6/2017, 3:29 PM

83.

84.

85.

86.

87.

The percentage of patients P who have survived t years after initial diagnosis of a certain disease is modeled by the

function .P(t) = 100(0.5)t

(a) According to the model, what percent of patients survive year after initial diagnosis?1(b) What percent of patients survive years after initial diagnosis?4(c) Explain the meaning of the base in the context of this problem.0.5

(a) According to the model, % of patients survive year after initial diagnosis.1

(Type an integer or a decimal.)

(b) According to the model, % of patients survive years after initial diagnosis.4

(Type an integer or a decimal.)

(c) Explain the meaning of the base in the context of this problem. Select the correct choice below and fill in the answer box to complete your choice.

0.5

A. As each year passes, % of the previous survivors take the diagnosis.

B. As each year passes, % of the total patients have survived.

C. As each year passes, % of the previous year's survivors have survived.

The function

D(h) = 8 − 0.18h

can be used to find the number of milligrams D of a certain drug that is in a patient's bloodstream h hours after the drug has been administered. How many milligrams will be present after 1 hour? After hours?10

After 1 hour, there will be milligrams. (Round to two decimal places as needed.)

After hours, there will be milligrams. (Round to two decimal places as needed.)10

Change the exponential statement to an equivalent statement involving a logarithm.

16 = 42

The equivalent logarithmic statement is . (Type an equation.)

Change the logarithmic statement to an equivalent statement involving an exponent.

log 81 = x9

The equivalent exponential statement is . (Type an equation.)


h(x) = ln (x + 9)

The domain of is . h



39 of 60 10/6/2017, 3:29 PM

88.

89.

90.

91.

92.

Solve the equation. Write the answer in terms of the natural logarithm.

5 = 70.5x

The solution set is .(Type an exact answer. Simplify your answer. Use a comma to separate answers as needed.)

Solve the equation. Write the answer in terms of the common logarithm.

4 • 10 = 139 − x

The solution set is .(Type an exact answer in simplified form. Use a comma to separate answers as needed.)

Writing as a single logarithm results in which of the following expressions?log p − log q + 3 log ra a a


log a

3pr

q

log a

p

qr3

log ( )a p − q + 3r

log a

pr3

q

Write the expression as a sum and/or difference of logarithms. Express powers as factors.

, x 0logx(x + 3)

(x + 5)13>

(Simplify your answer.)logx(x + 3)

(x + 5)13=

Solve the following logarithmic equation.

2 log (x − 8) + log 2 = 32 2


A. The solution set is . (Simplify


your answer. Type an exact answer. Use a comma to separate answers asneeded.)


40 of 60 10/6/2017, 3:29 PM

93.

94.


log x + log (x + 15) = 2





log (8x + 5) = 1 + log (x − 5)




your answer. Type an exact answer. Use a comma to separate answers asneeded.)

your answer. Type an exact answer. Use a comma to separate answers as needed.


41 of 60 10/6/2017, 3:29 PM

95.A chemist has a 100-gram sample of a radioactive material. He records the amount of radioactive material every week for 6 weeks and obtains the following data.

Week, xWeight, y(in grams)

0 100.0

1 84.0

2 68.7

3 59.8

4 48.5

5 40.4

6 33.8

(a) Treating week, x, as the independent variable, use a graphing utility to fit an exponential function to the data.

y = abx =

(Round to four decimal places as needed.)

(b) Express the function found in

part (a) in the form A(t) = A .0kt

A(t) =

(Round to four decimal places as needed.)

(c) Graph the data together with the exponential function found in part (a) or part (b) on a scatter diagram.

Which graph correctly illustrates the exponential model found for this data?

A.

-1

20

B.

-1

20

C.

-1

20

(d) From the result found in part (b), determine the half-lifeof the radioactive material.

The half-life of the material is about weeks.

(Round to one decimal place as needed.)

(e) How much radioactive material will be left after weeks?

30

After weeks, about gram(s) of

radioactive material will be left.

30

(Round to two decimal places as needed.)

(f) When will there be grams of radioactive material?10

There will be grams of material left after about

weeks.

10

(Round to one decimal place as needed.)


42 of 60 10/6/2017, 3:29 PM

96.

97.

Solve the system of equations. If the system has nosolution, say that it is inconsistent. Graph the lines of the system.

x + y = 7

x − y = 1

Select the correct choice below and, if necessary, fill in any answer boxes within your choice.

A. The solution is x and

y . (Type integers or

simplified fractions.)

=

=

B. There are infinitely many solutions. Using ordered pairs, they can be expressed as

(x,y)| x = , y is any real number .(Simplify

C. The system is inconsistent.

Use the graphing tool to graph the lines.

Solve the system of equations. If the system has no solution, say that it is inconsistent.

x + 3y = 9

2x + 6y = 18


A. The solution is x and y . (Type integers or simplified

fractions.)

= =

B. There are infinitely many solutions. Using ordered pairs, they can be expressed as .(x,y) x = y any real number

(Simplify

C. The system is inconsistent.

your answer. Type an expression using y as the variable asneeded.)

,

your answer. Type an expression using y as the variable as needed.)


43 of 60 10/6/2017, 3:29 PM

98.

99.

Solve the given system of equations. If the system has no solution, say that is it inconsistent.

x − y = 4

2x − 5z = 14

2y + z = 6


A. The solution is x , y , and z . (Type

integers or simplified fractions.)

= = =

B. There are infinitely many solutions. Using ordered triplets, they can be expressed as .(x,y,z) x = y = z any real number

(Simplify

C. There are infinitely many solutions. Using ordered triplets, they can be expressed as .(x,y,z) x = y any real number, z any real number

(Simplify

D. The system in inconsistent.

Solve the system of equations. If the system has no solution, say that it is inconsistent.

x − y − z = 1

− x + 2y − 2z = − 5

3x − y − 9z = − 5


A. The solution is x , y , and z . (Type

integers or simplified fractions.)

= = =

B. There are infinitely many solutions. The solution set is .(x,y,z) x = y = z is any real number

(Simplify

C. There are infinitely many solutions. The solution set is .(x,y,z) x = y is any real number, z is any real number

(Simplify your answer. Type an expression using y and z as the variables.)

D. The system is inconsistent.

, ,

your answers. Type expressions using z as the variable as needed.)

,

your answer. Type an expression using y and z as the variables as needed.)

, ,

your answers. Type expressions using z as the variable.)

,


44 of 60 10/6/2017, 3:29 PM

1. A. ( − 2,0),(3,0),(0, − 6) (Type an ordered pair. Use a comma to separate answers as needed.)

No

No

No

2. A. The intercept(s) is/are .(0,0) (Type an ordered pair. Use a comma to separate answers as needed.)

No

No

Yes

3.

y − 4 = 4(x − 8)

4. (2,1)

5

A. The intercept(s) is/are .2 − 2 ,0 , 2 + 2 ,0 , 0,1 − , 0,1 +6 6 21 21

(Type an ordered pair. Use a comma to separate answers as needed. Type exact answers for each coordinate, using

radicals as needed.)


45 of 60 10/6/2017, 3:29 PM

5. Domain : { }Abby, Beni, Geby, Saul, Makin Range : { }Hattie, Bud, Rosa, Zena

C. Yes, because each element in the first set corresponds to exactly one element in the second set.

6. − 9,3,7

5,6,12

B.

The relation is not a function because there are ordered pairs with as the first element and different second elements.3

7. − 3, − 2, − 1,0

0,1,4

A.

The relation is a function because there are no ordered pairs with the same first element and different second elements.

8. − 3

61

29

3x − 4x − 32

− 3x − 4x + 32

3x + 10x + 42

48x + 16x − 32

3x + 6hx + 3h + 4x + 4h − 32 2

9.−

7

8

13

−1

17

− 6x + 7

− 9x − 8

−6x + 7

9x − 8

6x + 19

9x + 10

30x + 7

45x − 8

6x + 6h + 7

9x + 9h − 8


46 of 60 10/6/2017, 3:29 PM

10. ( − , − 5) ( − 5, 5) (5, )

11. ( − ,0) (0, )

12. [8, )

13. x > − 4

14. (5, )

15. 9x + 1


− 5x + 5


14x + 17x − 62


2x + 3

7x − 2

A. The domain is .x x ≠2

7

(Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)

19

− 10

286

1

16. 2x + h − 4

17. − 4,7


47 of 60 10/6/2017, 3:29 PM

18. − 2

2

2

− 1

Negative

Positive

− 18, − 3,12

− 18 < x < − 3,12 < x ≤ 18

− 21 ≤ x ≤ 18

− 2 ≤ y ≤ 3

− 18, − 3,12

− 1

3

1

− 21,6

− 9

19. − 1

− 9

− 7

7

0

4

5

20. Yes

21. ( − 7,7)

22. Yes

A. The local is y .maximum = 4 (Type an integer.)

23. A. x = − 6, 2 (Type an integer. Use a comma to separate answers as needed.)

A. The local are .minima − 4, − 4 (Type an integer. Use a comma to separate answers as needed.)

24. A. The absolute of f is maximum f = .− 6 6 (Type integers or fractions.)


48 of 60 10/6/2017, 3:29 PM

25. A. The value(s) of x at which f has a local maximum is/are x .= 0


A. The local maxima is/are y .= 3 (Type an integer. Use a comma to separate answers as needed.)

A. The value(s) of x at which f has a local minimum is/are x .= − 2,1


A. The local minima is/are y .= 0,0 (Type an integer. Use a comma to separate answers as needed.)

26. A. x =2


A. 3 (Type an exact answer, using as needed. Use a comma to separate answers as needed.)

A. x = −2


A. − 3 (Type an exact answer, using as needed. Use a comma to separate answers as needed.)

27. Even

28. Even

29. − 20

4

− 6

30. 5

y = 5x − 36

31. Odd

54

32. C. y = x

33. Cube function

34. Reciprocal function


49 of 60 10/6/2017, 3:29 PM

35.

B.

36. ( − , )

A. The intercept(s) is/are .(0,4) (Type an ordered pair. Use a comma to separate answers as needed.)

D.

[1, )

A. Yes, f is continuous on its domain.

37. ( − , )

A. The intercept(s) is/are .( − 4,0),(0,0) (Type an ordered pair. Use a comma to separate answers as needed.)

B.

( − , )

A. No, f is discontinuous at x .= 0 (Use a comma to separate answers as needed.)


50 of 60 10/6/2017, 3:29 PM

38.

( − , )

( − , )

39.

B.

[ − 2, )

[0, )

40.

C.

B.


51 of 60 10/6/2017, 3:29 PM

41.x

5

4

A.

C. y = 1.2x + 1

A.

42. 4x + 187

D.

C. y = 3.8613x + 187.0146

A.

43.

B.


52 of 60 10/6/2017, 3:29 PM

44.

45.

C.

− 2,4

( − 2, − 5),(4,7)

F.

46. 4,500,000

47. 3025

64

31185

128

199

C.

164

48. A. The solution set is .( − 7, − 2)

(Type your answer in interval notation. Use integers or fractions for any numbers in the expression.)


53 of 60 10/6/2017, 3:29 PM

49. A. The solution set is .( − ,0) (4, )


50. A. The solution set is .( − , − 6) (2, )


51. ( − , − 8] [8, )

52. A. It is a polynomial of degree .4 (Type an integer or a fraction.)

A.

The polynomial in standard form is G(x) with leading term and constant

.

= 4x − 8x + 16x − 24x + 124 3 2 4x4

12

(Simplify your answers. Use integers or fractions for any numbers in the expressions.)

53. x − 9x − 9x + 813 2

54. x − 2x − 15x3 2

55. 2x − 12x − 2x + 603 2

56. A. The real zero(s) of f is/are .5, − 7

(Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression. Use a

comma to separate answers as needed.)

1

2

(1) crosses

(2) touches

2

− 8x3


54 of 60 10/6/2017, 3:29 PM

57. − x3

− 2,0,2

0

− 2,0,2

1

(1) crosses

− 2

1

(2) crosses

0

1

(3) crosses

2

2

C.

58. B. f(x) = − 2(x + 3)(x − 1)(x − 4)2

59. A. The domain of R(x) is {x | }.x ≠ − 9

(Type an inequality. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as

needed.)

60. A. The domain of H(x) is {x | }.x ≠ 4,x ≠ − 3

(Type an inequality. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as

needed.)

61. A. The vertical asymptote(s) is/are x .= − 15 (Use a comma to separate answers as needed.)

A. The horizontal asymptote(s) is/are y .= 18 (Use a comma to separate answers as needed.)



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62. A. The vertical asymptote(s) is/are x .= −3

2


A. The horizontal asymptote(s) is/are y .=5

2



63. B. There is no vertical asymptote.


A. The oblique asymptote(s) is/are y = .5x − 4


64. ( − , − 8) (3, )

65. ( − ,14)

66.C. − 1,1, − 11,11, − 121,121, − , , − , , − , , − , , − ,

1

11

1

11

1

5

1

5

1

55

1

55

11

5

11

5

121

5

121

5

67. A. x = − 5, − 1, 3

(Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions for any rational numbers

in the expression. Use a comma to separate answers as needed.)

(x + 1)(x + 5)(x − 3)

68. A. x = − 5,1,2, − 2

(Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions for any rational numbers

in the expression. Use a comma to separate answers as needed.)

(x + 5)(x − 1)(x + 2)(x − 2)

69. − 2

2

70. − 1

1100

Yes


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71. 3

x+ 4

72. − 1

− 1

8

0

8

− 5

73. 552

1029

64

105

74. x

x

Yes

75. Yes

76. Yes

77.3

x − 8





A.


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78.1 − 10x

x

A. The domain is .x x ≠ − 10

A. The range is .y y ≠ 0

C. The domain is .x x ≠ 0

B. The range is .y y ≠ − 10

D.

79. 31.489

31.524

31.541

31.544

80. 2

5

81. 8

82. 24

4

83. 50

6.25

C. As each year passes, % of the previous year's survivors have survived.50

84. 6.68

1.32

85. 2 = log 164

86. 81 = 9x


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87. ( − 9, )

88. ln 1.4

0.5

89.9 − log

13

4

90.log a

pr3

q

91. log x + log (x + 3) − 13 log (x + 5)

92. A. The solution set is . 10

(Simplify your answer. Type an exact answer. Use a comma to separate answers as needed.)

93. A. The solution set is . 5

(Simplify your answer. Type an exact answer. Use a comma to separate answers as needed.)

94. A. The solution set is .

55

2

(Simplify your answer. Type an exact answer. Use a comma to separate answers as needed.

95. 100.3022(0.8345)x

100.3022 − 0.1809t

A. -1

20

3.8

0.44

12.7


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96. A. The solution is x and y . (Type integers or simplified fractions.)= 4 = 3

97. B.

There are infinitely many solutions. Using ordered pairs, they can be expressed as

.(x,y) x = − 3y + 9 , y any real number

(Simplify your answer. Type an expression using y as the variable as needed.)

98. A.

The solution is x , y , and z . (Type integers or simplified fractions.)= 7 = 3 = 0

99. B.

There are infinitely many solutions. The solution set is

.(x,y,z) x = 4z − 3 , y = 3z − 4 , z is any real number

(Simplify your answers. Type expressions using z as the variable.)


60 of 60 10/6/2017, 3:29 PM

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