c. · -5 -4 5 16 x y b.-5 -4 5 16 x y c.-5 -4 5 16 x y d.-5 -4 5 16 x y solve for x. 27x=81 the...

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Student: _____________________ Date: _____________________

Instructor: roula dakdouk Course: Fall 2018 P Math 125 Dakdouk Assignment: Practice Test Ch 12 & 13

If and , find the following composition.f(x) = x − 6x + 22 g(x) = − 2x

(g ◦ f)(3)

(g ◦ f)(3) =

If f(x) and g(x) , find (f g)(x) and (g f)(x).= x + x − 93 = 2x ◦ ◦

(f g)(x) = ◦

(g f)(x)◦ =

Given the one-to-one function find the following. Hint: You do not need to find the equation for .f(x) = x + 53 f (x)− 1

a. f(4)b. f (69)− 1

a. Find the following value.

f(4) =

b. Find the following value.

f (69)− 1 =

The following function is one-to-one. Find the inverse of the function and graph the function and its inverse on the same set of axes.

f(x) x= 2 + 4

f (x)− 1 = (Type a simplified fraction. )

Use the graphing tool to graph the function and its inverse.

-10 -8 -6 -4 -2 2 4 6 8 10

-10

-8

-6

-4

-2

2

4

6

8

10

x

y

Find the inverse of the one-to-one function.

f(x) = (x − 1)3

(Type an exact answer, using radicals as needed.)f (x)− 1 =

6.

7.

8.

9.

10.

11.

12.

Graph the exponential function.

y = 3 + 3x

Choose the correct graph on the right.

A.

-5 5-4

16

x

y

B.

-5 5-4

16

x

y

C.

-5 5-4

16

x

y

D.

-5 5-4

16

x

y

Solve for x.

27x = 81

The solution is x .= (Simplify your answer.)

Solve the equation for x.

81 = 27(x + 3)

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

Suppose a city with population has been growing at a rate of % per year. If this rate continues, find the population of this city in years.

600,000 411

The population in years will be approximately . (Round to the nearest whole number as needed.)11

Find the value of the logarithmic expression.

log 164

log 164 =

Find the value of the logarithmic expression.

log 8164

log 8164

=

Solve.

log 81 = 4x

x =

13.

14.

15.

16.

Solve the equation for x.

log x9 =12

x =

Graph the logarithmic function. Find any intercepts.

y = log x10

Choose the correct graph.

A.

-5 5

-5

5

x

y

B.

-5 5

-5

5

x

y

C.

-5 5

-5

5

x

y

D.

-5 5

-5

5

x

y

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

A. The x-intercept is and the y-intercept is . (Type an ordered pair.)

B. The y-intercept is . There is no x-intercept.   (Type an ordered pair.)

C. The x-intercept is . There is no y-intercept.   (Type an ordered pair.)

D. There is no x- or y-intercept.

Write as a single logarithm. Assume that the arguments of all logarithms represent positive numbers.

5 log x + log x − 2 log (x + 1)614 6 6

5 log x + log x − 2 log (x + 1)614 6 6 =

(Simplify your answer, using fractional exponents as needed.)

Write the expression as a sum or difference of multiples of logarithms. Assume that variables represent positive numbers.

log 5x4

y

(Type all variables without any exponents.)log 5x4

y=

17.

18.

19.

20.

21.

22.

Find the exact value.

log 1

10,000

log 1

10,000=

Find the exact value.

ln 5e

(Type an integer or a simplified fraction.)ln 5e =

Solve the equation for x. Give an exact answer and a four-decimal-place approximation.

ln (3x − 4) = 1.4

The exact answer is x .= (Simplify your answer.)

A four-decimal place approximation is x .= (Round to four decimal places as needed.)

Approximate the logarithm to four decimal places.

log 35

log 35 = (Do not round until the final answer. Then round to four decimal places as needed.)

How much money does Dana Jones have after years if she invests $ at % interest compounded continuously? Use the formula to solve.

12 1500 5A = P e

rt

Dana Jones has $ after years.12 (Simplify your answer. Type an integer or a decimal. Round to the nearest cent as needed.)

Solve the equation. Give an exact solution, and also approximate the solution to four decimal places.

3 = 5x − 7

Write the exact solution.

x (Simplify your answer.)=

The approximate solution is . (Do not round until the final answer. Then round to four decimal places as needed.)

23.

24.

25.

26.

Solve the equation.

log x − 6x = 172

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

A. x = (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)

B. There is no solution.

Solve the equation.

log (x + 9) − log x4 4 = 3

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

A. x = (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)

B. There is no solution.

Solve the equation.

log x + log (3x + 5) = 12 2

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

A. x = (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)

B. There is no solution.

Use the formula A to solve the compound interest problem.= P 1 +rn

nt

Find how long it takes for $ to double if it is invested at % interest compounded monthly.700 3

The money will double in value in approximately years. (Do not round until the final answer. Then round to the nearest tenth as needed.)

27.

28.

The graph of the equation is a parabola. Find the vertex of the parabola and determine its graph.

x = (y − 2) + 22

Use the graphing tool to graph the parabola.

-10 -8 -6 -4 -2 2 4 6 8 10

-10

-8

-6

-4

-2

2

4

6

8

10

The graph of the equation is a parabola. Find the vertex of the parabola and determine its graph.

y = − 2(x + 2) − 52

Use the graphing tool to graph the parabola.

-10 -8 -6 -4 -2 2 4 6 8 10

-10

-8

-6

-4

-2

2

4

6

8

10

29.

30.

31.

Find the center and the radius of the circle. Then graph the circle.

x (y )2 + − 4 2 = 16

Use the graphing tool to graph the circle.

-10 -8 -6 -4 -2 2 4 6 8 10

-10

-8

-6

-4

-2

2

4

6

8

10

x

y

Find an equation of the circle having the given center and radius.

Center ( , ), radius − 9 4 3 10

Choose the correct equation.

A. (x + 9) + (y − 4) = 302 2

B. (x + 9) + (y − 4) = 902 2

C. (x − 9) + (y + 4) = 902 2

D. (x − 9) + (y + 4) = 302 2

Sketch the graph of the equation.

+ = 1x2

9y2

4

Choose the correct graph on the right.

A.

-10 10

-10

10

x

y

B.

-20 20

-20

20

x

y

C.

-10 10

-10

10

x

y

D.

-20 20

-20

20

x

y

32.

33.

Sketch the graph of the equation.

− = 1y2

9x2

25

Choose the correct graph on the right.

A.

-10 10

-10

10

x

y

B.

-10 10

-10

10

x

y

C.

-10 10

-10

10

x

y

D.

-10 10

-10

10

x

y

Identify whether the equation, when graphed, will be a parabola, circle, ellipse, or hyperbola. Sketch the graph of the equation.

(x + 3) + (y + 5) = 162 2

Select the correct choice below and fill in the answer box(es) within your choice.

A. This is a hyperbola. The x- or y-intercepts are . (Type ordered pairs. Use a comma to separate answers as needed.)

B. This is a parabola. The vertex is . (Type an ordered pair.)

C. This is an ellipse. The center is . (Type an ordered pair.)

D. This is a circle. The center is . (Type an ordered pair.)

The radius is .

Use the graphing tool to graph the circle.

-10 -8 -6 -4 -2 2 4 6 8 10

-10

-8

-6

-4

-2

2

4

6

8

10

x

y

34.

35.

36.

Identify whether the equation, when graphed, will be a parabola, circle, ellipse, or hyperbola. Sketch the graph of the equation.

y2

9−

x2

36= 1

Select the correct choice below and fill in the answer box(es) within your choice.

A. This is a circle. The center is . (Type an ordered pair.)

The radius is .

B. This is a hyperbola. The x- or y-intercepts are . (Type ordered pairs. Use a comma to separate answers as needed.)

C. This is a parabola. The vertex is . (Type an ordered pair.)

D. This is an ellipse. The center is . (Type an ordered pair.)

Choose the correct graph below.

A.

-10 10

-10

10

x

y

B.

-10 10

-10

10

x

y

C.

-10 10

-10

10

x

y

D.

-10 10

-10

10

x

y

Identify whether the equation, when graphed, will be a parabola, circle, ellipse, or hyperbola. Sketch the graph of the equation.

x = y − 8y + 142

Select the correct choice below and fill in the answer box(es) within your choice.

A. This is a circle. The center is . (Type an ordered pair.)

The radius is .

B. This is a hyperbola. The x- or y-intercepts are . (Type ordered pairs. Use a comma to separate answers as needed.)

C. This is a parabola. The vertex is . (Type an ordered pair.)

D. This is an ellipse. The center is . (Type an ordered pair.)

Use the graphing tool to graph the parabola.

-10 -8 -6 -4 -2 2 4 6 8 10

-10

-8

-6

-4

-2

2

4

6

8

10

x

y

Solve the nonlinear system of equations for real solutions.

5x2 + 3y2 = 32

− x2 + y2 = 8

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

A. The solution(s) is(are) . (Type an ordered pair. Use a comma to separate answers as needed.)

B. There is no solution.

37.

38.

Graph the inequality.

y (x )> + 1 2 − 3

Use the graphing tool to graph the inequality.

-10 -8 -6 -4 -2 2 4 6 8 10

-10

-8

-6

-4

-2

2

4

6

8

10

x

y

Graph the system.

y x> 2

y x≥ 2 + 2

Use the graphing tool to graph the system.

-20 -16 -12 -8 -4 4 8 12 16 20

-20

-16

-12

-8

-4

4

8

12

16

20

x

y

39.

40.

Graph the system.

x2 +y2

25 ≥ 1

x2 + y2 ≥ 1

Choose the correct graph below.

A.

-6 6

-6

6

x

y

0

B.

-6 6

-6

6

x

y

0

C.

-6 6

-6

6

x

y

0

D.

-6 6

-6

6

x

y

0

The graph of the equation is a parabola. Find the vertex of the parabola and determine its graph.

y = − 4(x − 3) + 52

Use the graphing tool to graph the parabola.

-10 -8 -6 -4 -2 2 4 6 8 10

-10

-8

-6

-4

-2

2

4

6

8

10

41.

42.

43.

The graph of the equation is a parabola. Find the vertex of the parabola and determine its graph.

y = x − 4x − 12

Use the graphing tool to graph the parabola.

-10 -8 -6 -4 -2 2 4 6 8 10

-10

-8

-6

-4

-2

2

4

6

8

10

Graph the inequality.

x y2 + 2 ≥ 25

Use the graphing tool to graph the inequality.

-10 -8 -6 -4 -2 2 4 6 8 10

-10

-8

-6

-4

-2

2

4

6

8

10

x

y

Sketch the graph of the equation.

+ = 1(x − 5)2

16(y − 3)2

9

Choose the correct graph on the right.

A.

-10 10

-10

10

x

y

B.

-10 10

-10

10

x

y

C.

-10 10

-10

10

x

y

D.

-10 10

-10

10

x

y

1. 14

2. 8x + 2x − 93

2x + 2x − 183

3. 69

4

4. x − 42

-10 -8 -6 -4 -2 2 4 6 8 10

-10

-8

-6

-4

-2

2

4

6

8

10

x

y

5. + 13 x

6.

D. -5 5-4

16

x

y

7. 43

8.−

94

9. 923,672

10. 2

11. − 2

12. 3

13. 3

14. B.

-5 5

-5

5

x

y

C. The x-intercept is . There is no y-intercept.  (Type an ordered pair.)(1,0)

15.

log 6x

214

(x + 1)2

16. 4 log x − log y5 5

17. − 4

18. 15

19. 4 + e1.4

3

2.6851

20. 0.6826

21. 2733.18

22.7 +

log 5log 3

8.4650

23. A. x = 7, − 1 (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)

24. A. x =17

(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)

25. A. x =13

(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)

26. 23.1

27.

-10 -8 -6 -4 -2 2 4 6 8 10

-10

-8

-6

-4

-2

2

4

6

8

10

28.

-10 -8 -6 -4 -2 2 4 6 8 10

-10

-8

-6

-4

-2

2

4

6

8

10

29.

-10 -8 -6 -4 -2 2 4 6 8 10

-10

-8

-6

-4

-2

2

4

6

8

10

x

y

30. B. (x + 9) + (y − 4) = 902 2

31.

A.

-10 10

-10

10

x

y

32.

B.

-10 10

-10

10

x

y

33. D. This is a circle. The center is . (Type an ordered pair.)( − 3, − 5) The radius is .4

-10 -8 -6 -4 -2 2 4 6 8 10

-10

-8

-6

-4

-2

2

4

6

8

10

x

y

34. B. This is a hyperbola. The x- or y-intercepts are .(0,3),(0, − 3) (Type ordered pairs. Use a comma to separate answers as needed.)

B.

-10 10

-10

10

x

y

35. C. This is a parabola. The vertex is . (Type an ordered pair.)( − 2,4)

-10 -8 -6 -4 -2 2 4 6 8 10

-10

-8

-6

-4

-2

2

4

6

8

10

x

y

36. A. The solution(s) is(are) . (1,3),(1, − 3),( − 1,3),( − 1, − 3) (Type an ordered pair. Use a comma to separate answers as needed.)

37.

-10 -8 -6 -4 -2 2 4 6 8 10

-10

-8

-6

-4

-2

2

4

6

8

10

x

y

38.

-20 -16 -12 -8 -4 4 8 12 16 20

-20

-16

-12

-8

-4

4

8

12

16

20

x

y

39.

B.

-6 6

-6

6

x

y

0

40.

-10 -8 -6 -4 -2 2 4 6 8 10

-10

-8

-6

-4

-2

2

4

6

8

10

41.

-10 -8 -6 -4 -2 2 4 6 8 10

-10

-8

-6

-4

-2

2

4

6

8

10

42.

-10 -8 -6 -4 -2 2 4 6 8 10

-10

-8

-6

-4

-2

2

4

6

8

10

x

y

43.

C.

-10 10

-10

10

x

y