MAT 135

In Class Assignments

MAT135

In-Class Assignment

2

Introduction to Set Notation

Set Notation and Definitions

A set is a collection of objects.

The members or objects in a set are called elements.

There are three ways to describe a set:

1. We can use words.

2. We can make a list.

3. We can use set-builder notation.

Some Notation

Union

Intersection

Is an element of:

Is not an element of:

Examples of Sets

1. Words:

N is the set of natural numbers or counting numbers.

2. List:

N = {1, 2, 3, …}

3. Set-builder notation:

N = {x | x N}

MAT135

In-Class Assignment

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Introduction to Set Notation (continued)

Examples of Sets

A={1,2,3} B={1,4,5}

1,2,3,4,5A B

1A B

2

2

A

B

Examples of Sets

A={1,2,3} B={5,6,7}

The Empty Set is the set containing no elements. It may be denoted by

1,2,3,5,6,7A B

???A B

1. List the elements in each set:

a. | is a natural number and 5A x x x

b. | is an odd whole number and 11B x x x

c. | is an integer and 5C x x x

2. Find the union of the sets:

a. 1,3,7,8 2,3,8

b. 1,3,7 2,4,8

c. , , , , , ,r e a l e a s y

MAT135

In-Class Assignment

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Introduction to Set Notation (continued)

3. Find the intersection of the sets:

a. 1,2,3,4 2,4,5

b. 1,3,7 2,4,8

c. , , , ,w h y h o w

4. Let 1,2,3,4,5,6 2,4,6,9,11,12A B .

Are the following statements true or false?

a. 6 A

b. 6 B

c. 2,4,6A B

d. 6 A B

e. A B

f. 1,2,3,4,5,6,9,11,12A B

g. 12 A

h. 5 A

i. 9 B

j. 8 B

5. Write the following in set-builder notation:

a. 1,2,3,4A

b. 4, 3, 2, 1,0A

MAT135

In-Class Assignment

5

Section 2.1 Solving Linear Equations

1. Solve the following equations:

5) 4 8 3 7 ) 3 23

3

1 1 1 5)7 3( 2) 4( 1) )

2 4 3 4

) (3 2) 26 )2 3(3 5) 6

a a a b t

c x x d x x

e x x f x x

2. The taxi meter was invented in 1891 by Wilhelm Bruhn. Chicago charges $1.80 plus

$0.40 per mile for a taxi ride.

a) If the fare is $6.60, write an equation that shows how the fare is calculated.

b) How many miles were traveled if the fare was $6.60?

3. In 1992, twice as many people visited their doctor because of a cough than an earache.

The total number of doctor’s visits for these two ailments was reported to be 45 million.

a) Let x represent the number of earaches reported in 1992. Write an expression for the

number of coughs reported in 1992.

b) Write an equation that relates 45 million to the variable x.

c) How many people visited their doctor in 1992 to report an earache?

MAT135

In-Class Assignment

6

Section 2.2 Formulas and Functions

1. Solving for a Variable

Although you can’t print most of these out without signing up at the site, there are some

useful presentations to help with this topic.

http://www2.guhsd.net/algebra2/Alg2Show/Chapter01/1_5LiteralEquations.htm

http://www.slideshare.net/crainsberg/solving-literal-equations

http://www.scribd.com/doc/6932127/Algebra-1-Notes-YORKCOUNTY-FINAL-Unit-3-

Lesson8-Solving-Literal-Equations

2. For each formula, express y as a function of x, then find y given that 2x .

a. 3 6x y

b. 4 5 10x y

c. 1

43

x y

d. 2 3 5x y

3. Solve for the indicated variable:

a. for p q rs t r

b. for x u v r y v

c. 2( ) for P l w w

d. 1 2 1( ) for A s r r r (Lateral area of a frustrum)

e. 1 2 1

1( ) for

2A h b b b (Area of a trapezoid)

MAT135

In-Class Assignment

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Section 2.3 Applications

Choose the equation that best describes the situation.

1.

2.

3.

4.

5.

MAT135

In-Class Assignment

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Section 2.3 Applications (continued) 6.

7.

8.

9.

10.

You may also want to view http://www.slideshare.net/ejboggs/translating-algebra

MAT135

In-Class Assignment

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Section 2.4 Inequalities

1. Solve the inequalities, graph each solution, and write the solution in interval notation:

1) y>4 ) 12 2

3

1)5 115 )10 y 36

2

)2(3 1) 10 )1 3 4(3 1)

a b x

c x d

e x f a

2. A store selling art supplies finds that x sketch pads are sold each week at a price of p

dollars each according to the formula x=900-300p. What price should they charge if they

want to sell:

a) at least 300 pads each week?

b) fewer than 525 pads each week?

c) more than 600 pads each week?

d) at most 375 pads each week?

3. What about the solutions to these problems?

a. 2 3 2( 4)x x

b. 4 3x x

c. 6 4 4 7x x

d. 2 4 5 4 2 1x x

MAT135

In-Class Assignment

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Section 2.5 Compound Inequalities

1. Solve the following inequalities. Use a line graph and interval notation to write each

solution set.

) 60 20 20 60 )7 5 2 or 3 2 3

1 2)5 x+1<9 )8 12 and >1

4 3

)3 1 2 4 or 5 2 3 4

a a b x x

c d x x

e x x x x

) 2 5 2f m

2. A factory’s quality control department randomly selects a sample of 5 lightbulbs to test.

In order to meet quality control standards, the lightbulbs in the sample must last an average

of at least 950 hours. Four of the selected bulbs lasted 925 hours, 1000 hours, 950 hours,

and 900 hours. How many hours must the fifth lightbulb last for the sample to meet quality

control standards?

3. A worker earns $12 per hour plus $16 overtime pay for every hour over 40 hours. How

many hours of overtime are needed to make between $600 and $800 per week?

4. Write each union or intersection as a single interval, if possible.

. 6, 8, . 6, 8,

. 6,10 4,12 . 5, , 8

a b

c d

MAT135

In-Class Assignment

11

Section 2.6 Absolute Value Equations and Inequalities

Some tutorials:

http://www2.bc.cc.ca.us/mperrone/LECTURES_PDF/Ch4/Microsoft%20PowerPoint%20-

%20bia5e_ppt_4_3.pdf

http://www.purplemath.com/modules/absineq.htm

1. Solve: 2 2 2 3 13x .

a. {-5} b. {3 } c. {-5 , 3} d. no solutions

2. Find all real solutions: 1 2 1x x .

a. {-2 } b. {-2 , 0} c. {0} d. no solutions

3. Find all real solutions: 3 3 18.x

a. 3x b. 3, 9x x c. 9, 3x x d.

4. Find all real solutions to the equation. 1 42 2x .

a. -4 b. no solutions c. 4 d. all real numbers

5. Solve the inequality: 2 43 4x .

a. ( , 7/3) b. (7/3 , ) c. (-7/3 , 7/3) d. ( , )

6. Solve the inequality: 1 2x .

a. [3 , ) b. ( , -1] U [3 , ) c. (- , -1] d. (- , )

MAT135

In-Class Assignment

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Section 2.6 Absolute Value Equations and Inequalities

(continued)

7. Solve the inequality: 8 8x .

a. 0,16 b. ( , 0) U (16 , ) c. (0,16) d.

8. Find all real solutions to the equation with absolute value. 8 3 137x .

a. 3 9

,8 8

b. 3

8 c.

9 3,

8 8 d.

9. Solve the inequality: 13 52

x.

a. 2,6 b. ( , -2] U (6 , ) c. 6, 2 d. ( , -6] U (2 , )

10. Solve the inequality: 11 33

113

x.

a. 6,6 b. ( , -6) U (6 , ) c. 6,0 d. ( , -6) U (0 , )

For more problems and answers:

http://www.analyzemath.com/AbsEqIneq/AbsEqIneq.html

MAT135

In-Class Assignment

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Section 3.1 The Coordinate Plane

1. The x-axis on the graph below represents number of hours worked and the y-axis

represents pay, in dollars. Approximately what is the pay for working 10, 20, 30, and 40

hours? Create a table that displays the data shown on the graph.

y

x

2. Find the x- and y-intercepts and graph the line.

a. 2 5 1x y

b. 3 0x y

c. 5x y

d. 2 5 20x y

3. Complete the ordered pairs so that the equation is satisfied.

a. 2 3 ( 2, ) ( , 7)y x

b. 5 6 ( 4, ) ( ,11)y x

c. 1 (8, ) ( , 3.5)1

2y x

d. 9 2 (3, ) ( ,16)y x

MAT135

In-Class Assignment

14

Section 3.2 Slope of a Line

1. Find the slope of the line from the given graphs:

y y

2. Find the slope of the line through the given points. Then plot each pair of points and

draw the line through them.

a) (2,1) (4,4) b) (2, -5) (3, -2) c) (1,5) (-4,-5)

3. A line, l, contains the points (3,4) and (-3,1). Give the slope of any line perpendicular

to l.

4. Determine if the line through the points (7,2) and (-9,2) and the line through the points

(4,-4) and (1, -4) are parallel, perpendicular, or neither.

5. Solve for y: 0

y bm

x

x x

MAT135

In-Class Assignment

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Section 3.3 Equation of a Line

1. What is the slope of the line whose equation is 3 4 16 0x y ?

[A] 3/4 [B] 4/3 [C] 3 [ D] 4

2. What is the equation of a line passing through the points (1,2) and (-2,5)?

[A] y = x + 3 [B] 3y x [C] 7

13

y x [D] y = 3x + 3

3. Which of the following is the equation of a line with a slope of 0 and passing through the point (4,6)?

[A] x = 4 [B] 4x [C] y = 6 [D] 6x

4. What is the slope of a line passing through the points (3,5) and (-2,6)?

[A] 1

5 [B] 1 [C] 5 [D]

11

5

5. A horizontal line has a slope of

[A] 0 [B] 1 [C] -1 [D] undefined

6. What is the slope of the line shown in the figure at the right?

[A] 4/3

[B] 3/4

[C] 3

4

[D] 4

3

7. What are the coordinates of the y-intercept of the equation y - 3x = 5?

[A] (0,3) [B] (0,-3) [C] (0,5) [D] (0,-5)

MAT135

In-Class Assignment

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Section 3.3 Equation of a Line (continued)

8. The slope of a vertical line is

[A] 0 [B] 1 [C] 1 [D] undefined

9. Find the slope of a line perpendicular to the line whose equation is 3y + 2x = 6.

[A] 2

[B] 2 [C] 3

2

[D] 3/2

10. Find the equation of the line parallel to the line whose equation is 3 5y x and whose

y-intercept is (0, 5) .

[A] 3 5y x [B] 3 5y x [C] 1 53

y x [D] 135

y x

11. Write an equation for a line passing through the points (c, 2b) and (c, 3b).

[A] y cx b [B] y cx b [C] 2x b [D] x c

12. Which is the equation of a line whose slope is undefined?

[A] 5x [B] 7y [C] x = y [D] x + y = 0

13. What is the equation of the line shown in

the graph at the right?

[A] 1

32

y x

[B] y = 2x - 3

[C] 1

32

y x

[D] 2 3y x

14. Which of these equations represents a line parallel to the line 2 6x y ?

[A] 2 3y x [B] 2 4y x [C] 2 8x y [D] 2 1y x

MAT135

In-Class Assignment

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Section 3.3 Equation of a Line (continued)

15. Find the equation of the line that has a slope of 2 and a y-intercept of (0, 9) .

[A] 2 9y x [C] 2 9y x

[B] 2 9y x [D] 2 9y x

16. Use the table at the right to answer the following questions:

a. Does Y1 pass through the origin?

b. What is the x-intercept of Y2?

c. For which values of x is Y1=Y2?

d. The graph of Y2 is in which quadrants?

e. The graph of Y1 is in which quadrants?

17. Write the general form of the equation of a line satisfying the given conditions.

a. 1

2,0 ,3

m b. 4, 2 , 0m

c. 3,2 , is undefinedm d. 0, 3 , 4m

18. Find the equation of a line with an x-intercept of (2,0) and a y-intercept of (0,3).

19. Complete the table:

Equation Slope, m x-intercept y-intercept

3 5y x

2y x

4 6 24x y

1y

3x

X Y1 Y2

-3 -5 - 9

-2 - 4 - 4

-1 - 3 - 1

0 - 2 0

1 - 1 - 1

2 0 - 4

3 1 - 9

MAT135

In-Class Assignment

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Section 3.3 Equation of a Line (continued)

20. Match the graph with its description. You may assume that each tick mark represents

one unit.

A. B.

C. D.

E. F.

1. This line has a slope of zero.

2. This line has a negative slope.

3. This line has an undefined slope.

4. This line is parallel to the line y = x.

5. This line has a positive y –intercept.

6. This line has a negative y –intercept.

x x

x x

x x

y y

y y

y y

MAT135

In-Class Assignment

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Section 3.5 Functions and Relations

1. Determine whether the relation is a function. Identify the domain and the range.

){(1,3)(2,5)(4,1)} ){(5, 2)(3, 2)(5, 1)} ){(3,1)(5,7)(2,3)}a b c

d) 3,1 , 5,1 , 7,1 e) 5,0 , 3, 1 , 0,0 , 5, 1 , 3, 2

2. Let 2( ) 2 5 and ( ) 3 4f x x g x x x . Evaluate:

) (2) ) ( 3) ) ( 2) ) (0)

) (2) (3) ) (2 ) ) (3 )

a f b f c g d g

e f g f g t g f a

3. The function ( ) 3300 18,000V t t where V is value and t is time in years can be used

to find the value of a large copy machine during the first 5 years of use.

a) What is the value of the copies after 3 years and 9 months?

b) What is the salvage value of the copier if it is replaced after 5 years?

c) State the domain of this function.

d) Sketch a graph of this function, clearly labeling values and the axes of the graph.

e) What is the range of this function?

f) After how many years will the copier be worth only $10,000?

4. A graph of a function, f, is shown. Find ( 2), (0), 4f f f . Note the scales on the axes.

5. Determine whether the equation represents y as a function of x.

a. 23 4x y b. 2 1x y

x

y

MAT135

In-Class Assignment

20

Section 4.1-4.2 Solving Systems of Equations

Tutorials: http://regentsprep.org/regents/math/math-topic.cfm?TopicCode=syslin

http://people.hofstra.edu/Stefan_Waner/RealWorld/tutorialsf1/frames2_1.html

1. Which ordered pair is the solution to the given system of equations?

3 9

2 5

x y

x y

A. ( 3, 4) B. (9, 3) C. (6, 1) D. (3, 2)

2. Solve the system of equations given by 2 2y x and 1

53

y x .

A. no solution B. (4, 6) C. ( 3, 4) D. infinitely many solutions

3. A store sells sheets for either $15 or $30. One month, sales totaled $12,570. If the store

sold 563 sheets, how many $15 sheets were sold?

4. The difference of the measures of two complementary angles is 6 degrees. Find the

measure of each angle. (Complementary angles add up to 90 degrees).

5. Solve the following systems:

a.

31

5

41

5

x y

x y

b. 2 3 6

2 3 8

a b

a b

c. 9 5 9

9 5 9

x y

x y d.

2 5 7

6 5 3

a b

a b

MAT135

In-Class Assignment

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Section 4.1-4.2 Solving Systems of Equations (continued)

6. The graph below gives the solution to which system of equations? You may assume

that each tick mark represents one unit.

A. 1

1

y x

y x B.

1

3

y x

y x C.

2 1

2 1

y x

y x D.

11

23

y x

y x

7. What is true of the graph below? There may be more than one answer.

A. The graph represents a system of equations that is inconsistent.

B. The graph represents a system of equations with infinitely many solutions.

C. The graph represents a system of equations with no solution.

D. Both of these lines have positive slope.

y

x

x

y

MAT135

In-Class Assignment

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Section 4.1-4.2 Solving Systems of Equations (continued)

8. Find the graph of the system. Use the graph to determine if the system is consistent or

inconsistent. If the system is consistent, determine the number of solutions.

x y

y x

RST4

2 7

A.

x

y

B.

x

y

Consistent, infinitely many solutions Consistent, one solution

C.

x

y

D.

x

y

Consistent, infinitely many solutions Inconsistent

9. A group of 51 people attend a ball game. There were twice as many children as adults in

the group. Set up a system of equations that represents the numbers of adults and children

that attended the game and solve the system to find the number of children that were in the

group.

A. a c

c a

RST51

2 51

34 children

B. a c

c a

RST51

2

17 children

C. a c

c a

RST51

2

34 children

D. a c

c a

RST51

2 51

17 children

MAT135

In-Class Assignment

23

Section 5.3 Polynomials and Polynomial Functions

1. Evaluate each polynomial for the given value of the variable:

2

3 2

)2 7 6 2 3

)8 2 1 0

a x x x x

b x x x x

2. Add or subtract as indicated:

a) Subtract 4 3 26 9 2 5 2a a a a from 4 310 12 7a a a

b) Add 4 3 23 7 8 10,a a a a 38 1,a and 2 410 9 7a a a .

c) (3 5) (3 5)x x

d) 6 { 2 6[2 3( 1) 6]}a a a a

e) 2 2 2 2 2 2(11 3 2 ) (9 2 ) ( 6 3 5 )x xy y x xy y x xy y

f) 2 2 2 2(2 7) ( 3) ( 7)m n mn mn m n

3. Which expression is not a polynomial?

A. 23 5x B.

37x C.

2 3

3

x D.

3 73x x

x

4. What is the degree of 3a – 4a2b

3 + b

3 – 4ab?

A. 1 B. 2 C. 3 D. 5

5. Write a polynomial to represent the area of a square with a side x minus the area of

a triangle with a base 2x and a height of 5.

A. 4x B. 2 5x x C.

2 2 5x x D. 2 10x x

MAT135

In-Class Assignment

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Section 5.3 Polynomials and Polynomial Functions

(continued)

6. Anthony and Sanford each throw a football. The height of Anthony's throw can

represented by the equation A = –10x2 + 15x + 22, where A is height and x is the time in

seconds. The height of Sanford's throw can represented by the equation

S = –9x2 + 14x + 23. At time x, how much higher is Sanford's throw?

A. x2 + x + 1 B. x

2 – x – 1

C. x2 + x – 1 D. x

2 – x + 1

7. Suppose the perimeter of a triangle is given by P = 13x + 5y, and two of its

sides have lengths of 2x + y and 8x + 4y. What is the length of the third side?

A. 23x+5y B. 6x + 3y C. 3x D. 3x + y

8. The calculated annual fixed cost (in dollars) of owning and operating an automobile is

given by the polynomial 220 45 5400x x , where x is the number of years after 1999. The

variable costs are represented by the polynomial 3 275 220 108 1550x x x . Find a

polynomial that represents the difference between the fixed cost and the variable cost for a

given year.

9. Multiply:

a. (2 3)( 4)x x =

b. (7 3)(4 1)x x

c. (3 3)(3 3)x x

d. (6 10)(10 6)x x

e. (2 3)(2 3)x x

MAT135

In-Class Assignment

25

Section 5.4 Multiplying Binomials

1. Multiply as indicated:

2 2

2 3 3

2 4

2 2

)2 (6 5 4) )(4 1)

)2 ( ) )3( 1)( 2)( 3)

)( 4)( 6) )( 1)( 5)

)(2 3)(3 5)

a x x x g x

b a b a ab b h x x x

c x x i b a

d x x

2 2 2

)(3 10)(3 10)

1)(2 )(4 2 ) )( )

2

)(5 3 )(4 2 )

j t t

e x y x xy y k q p

f t t

2. For (a) and (b) below, find ( ) ( )f x g x , ( 2)f a , and ( 1) ( )g x g x :

a) 2 2( ) 3 2 and ( ) 2 1f x x g x x

2 2) ( ) 2 2 and ( ) 2 3b f x x x g x x x

Multiplying binomials:

http://www.regentsprep.org/Regents/math/math-topic.cfm?TopicCode=polymult

MAT135

In-Class Assignment

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Section 5.5-5.7 Factoring Polynomials

1. Factor out the greatest common factor:

3 2 2 2 2 2

3 2

2 2 2 2 2 2 2

)4 16 20 )

)5 ( 2 ) 3 ( 2 ) )10 (2 3 ) 15 (2 3 )

)20 30 25 )

)9

a x x x b x y xy x y

c x a b y a b d x x y x x y

e a b c ab c a bc f ax x bx ab

g 3 218 4 8 )2 ( 2) 3(2 )x x x h y x x

2. In a polygon with n sides, the interior angles, measured in degrees, add up to

180n -360. Find an equivalent expression by factoring out the GCF.

3. The area (in square meters) of a pool is given by the expression 2 30A l l , where l is

the length of the pool.

a) Factor the expression for the area.

b) The width of this pool is 20 m. What is the length?

4. Factor:

2 2

3 2 2 2

2 2 2

4 3 2

) 6 )3 3 6

)2 14 20 ) 10 25

) 8 9 )2 7 6

)6 2

a y y b a a

c x x x d x xb b

e m mn n f a a

g x x x 3 2 2

2 2 2

)60 28 16

) 21 70 49 )2 ( 5) 7 ( 5) 6( 5)

h p p q pq

i x xy y j x x x x x

MAT135

In-Class Assignment

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Section 5.5-5.7 Factoring Polynomials (continued)

5. Find the missing factor:

2

2 2

2

)12 8 ( )(6 )

) 2 48 ( 6 )( )

)2 15 ( 3)( )

a x x x

b x xa a x a

c x x x

6. Factor, if possible:

2 2 2

3 2 2 2

2 2 2

2

)12 17 2 )9 6 1

)2 4 96 ) 5 6

) 2 )9 6

) 6 - 8

a x xy y b a a

c x x x d x xb b

e m mn n f a a

g t t

7. Factor, if possible:

2 4 2

2 3 2

4 2

2 3

3

)25 10 ) 144

) 100 )27 36 12

) 81 )16( ) ( )

)( 2) 9 )50 18

) 8

a t t g x y

b x h m m m

c x i x y a x y

d x j xy x y

e a 4 2

2 2 2

2 2

)9 81

)36 60 25 )9 12 4

)9 60 100

k x y

f x x l a ab b

m pq p q

Summary of factoring polynomials:

http://itech.pjc.edu/falzone/handouts/factor_polynomials_steps4.pdf

MAT135

In-Class Assignment

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Section 5.5-5.7 Factoring Polynomials (continued)

True or False:

1. 29 16x is a prime polynomial.

2. 24 25x may be factored as a difference of two squares.

3. 225 30 9b b is a perfect square trinomial.

4. 23 22 7 ( 7)(3 1)b b b b .

5. 4 1y is a prime polynomial.

6. 2 24 16 4 4x x .

7. 2( 5) 9 ( 2)( 8)x x x

Choose the correct answer:

8. Factor 8a4b - 3a

2b

3c.

a. 8ab(a2 - 3bc) b. abc(8a

3 - 3b) c. a

2b(8a

2 - 3bc) d. ab(8a

3 - 3b

2c)

9. Factor 2r3 + 8r

2 - 10r completely.

a. 2(r3 + 4r

2 - 5r) b. (2r - 1)(r + 5) c. 2r(r - 1)(r + 5) d. 2r(r

2 + 4r - 5)

10. Factor m3 - 4m

2 + 6m - 24.

a. m(m2 - 4m + 6) – 24

b. m2(m - 4) + 6m – 24

c. (m - 4)(m2 + 6)

d. (m + 4)(m2 - 6)

MAT135

In-Class Assignment

29

Section 5.8 Solving Equations by Factoring

1. Solve each equation:

2 2

2 2

3

2

2

)9 12 0 )2 5 3 0

)3 4 0 )4 6 2

)16 25 )2 ( 7) 24

)800 100 )( 2)( 4) 12

)( 1) 3 7

a t t f x x

b x x g x x

c x x h n n

d x x i n n n

e x x

2. Find all values such that ( ) ( )f x g x :

2

2

2

) ( ) 10 35 ; ( ) 20

) ( ) 4 ; ( ) 1

) ( ) 18; ( ) 3

a f x v v g x

b f x y y g x y

c f x t g x t

3. A ball is dropped from a balloon 900 feet above the ground. The height, h, of the ball

above the ground (in feet) after t seconds is given by the equation 2900 16h t . When

will the ball hit the ground?

Self-quiz on solving quadratic equations:

http://teachers.henrico.k12.va.us/math/HCPSAlgebra1/Documents/examviewweb/ev8-

6.htm

Factoring Jepoardy: http://teachers.henrico.k12.va.us/math/HCPSAlgebra1/Documents/8-

Review/FactoringJeopardy.ppt

MAT135

In-Class Assignment

30

Section 6.1 Properties of Rational Expressions and Functions

1. Identify the value(s) for which the given expression is undefined: 2 2

2

2 1 3 2) ) )

5 6 3 2 3 5

x x t ba b c

t b b

2. Evaluate the expression 2

3

x

x for the given values of x: 2, 2, 3, 3x x x x .

3. Reduce to lowest terms:

3 2 2 5 2 5 3

4 3 8

2 12 16 2 3 28 9. . . .

6 24 8 2 14 18

x x x x y x x a ba b c d

x x y x a b

4. Fill in the expression that makes the rational expressions equivalent:

2 2

2 2

2

2 2

( 5) ? 9 ?. = .

4 5 -1 6 9 3

11 18 9 ?. = .

7 10 ? 1

x x xa c

x x x x x x

x x x y xb d

x x y xy y x y

5. Fill in the expression that makes the rational expressions equivalent: 2

2

2

2 ? 6 9 ?. = .

1 1 3 9

6 10 24 6 6 ?. = .

7 ? 6

x xa c

x x x x

x x x xb d

x x x

6. Find the domain in interval notation:

2

2 2 2

2 2 2 7 2 1. . . .

1 1 4 2 3

x x xa b c d

x x x x x

MAT135

In-Class Assignment

31

Section 6.2 Multiplication and Division of Rational Expressions

1. Perform the indicated operation and express the answers in lowest terms:

2

2

2

2

2 2

2 2 2

2 2

2

2 3

2 3

2 2 3 2

2 2

9 x-2)

4 x-3

5 1 1)

4 4 5 1

6 3)

2

7 12 9 18)

5 7 10

4 1 8 1)

6 2 27 8

12 3 42 6 15)

9 36

xa

x

x x xb

x x x

p q q p qc

p pq p pq q p

a a a ad

a a a

t te

t t t

a b ab b af

a b

2

3 4

2 2 2 2 2 2

2 2 2 2 2 2

6

8

16 9 20 25)

8 16 7 12 6 9

ab b

a b b

a b a ab b a bg

a ab b a ab b a ab b

2, For ( ) and ( )f x g x , find ( )

( ) ( ) and ( )

f xf x g x

g x:

2

2 2

2 2

1 5 6) ( ) ; ( )

6 1

7 12 9) ( ) ; ( )

3 4

y y ya f x g x

y y y

m m mb f x g x

m m

MAT135

In-Class Assignment

32

Section 6.2 Multiplication and Division of Rational Expressions

(continued)

3.

2 2

2 2

11 24 19 84

21 108 18 80

x x x x

x x x x

2 2

2 2

11 24 19 84 3( 3)( 7) ( 3)( 7). . . .( 9)( 10) ( 9)( 10) 1021 108 18 80

x x x x xx x x xa b c d

x x x x xx x x x

4.

224 144 10 120

5 60 50

x x x

x

22

2

24 144

12

12. 50 . . 1 .

25

x x

x

xa b c d

5.

2 23 9

3 3 9

x x

x x

222

2 2

6 93

3 3

( 3) 3( 3). . . .( 3) ( 3) 9

x

x

xx xa b c d

x x x

6.

2 2

2 2

5 6 15 56

10 16 10 21

x x x x

x x x x

3 1

78

( 8). . . 1 .( 7)

x

xx

xa b c d

x

7. Write an expression for the area and simplify:

2

in5

b

a

MAT135

In-Class Assignment

33

24in

a

b

Section 6.3 Addition and Subtraction of Rational Expressions

1. Find the least common denominator of 2 4 3

3 1 and

6 9x y x y.

2 2 3 4 3 4.18 . 54 .18 .54a x y b x y c x y d x y

2. Find the least common denominator of 2 2

6 6 and

9 18 4 3x x x x.

.( 6)( 3) . ( -3)( -1) .( 6)( 3)( 1) .( 6)( 3)( 1)a x x b x x c x x x d x x x

3. Write each expression using the LCD as the denominator: 5 3 3 5

3 2 and

5 25x y x y.

2 2 2 2

5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

3 2 15 2 15 2 15 2. , . , . , . ,25 25 25 25 25 25 25 25

x y y xa b c d

x y x y x y x y x y x y x y x y

4. Write each expression using the LCD as the denominator: 2 3 2

3 7 and

2 8 5 20t t t t.

2

2 2 2 2 2 2 2 2

3 14 15 7 3 14 15 14. , . , . , . ,10 ( 4) 10 ( 4) 10 ( 4) 10 ( 4) 10 ( 4) 10 ( 4) 10 ( 4) 10 ( 4)

t t t ta b c d

t t t t t t t t t t t t t t t t

5. Perform the indicated operation and simplify where possible:

2

3 2

8 2 5 7) )

3 3

3 2 4 2 2) )

4 4 1 3 12 4

1 18 2 8 3) )

2 3 8 27 3 8 4

a bx x p q q p

n n x xc d

n n x x

y x xe f

y y x x 2

2 2

3 5 2

6 1 4 3 4 3) )

2 1 1 2 1 8 16 2 ( 2)

x x

x x x y y yg h

x x x x y y y

MAT135

In-Class Assignment

34

Section 6.3 Addition and Subtraction of Rational Expressions

(continued)

6. Given ( ) and ( )f x g x ( ) ( ) and f ( ) ( )f x g x x g x :

2 2

3 3

9 6) ( ) ; ( )

9 6 8 9 4

1 3) ( ) ; ( )

a f x g xx x x

abb f x g x

a b a b

7. The formula 1 1

Pa b

is used by optometrists to determine how strong to make

eyeglasses. If a =10 and b =0.2, find the value of P.

8. Write an expression for the sum of the reciprocals of two consecutive integers and

simplify it.

9. Write an expression that represents the perimeter of the figure and simplify.

5

.3

mx

2

.5

xm

x

10. If a

b represents the probability of an event, then the probability that the event will not

occur is 1a

b. Write 1

a

b as a single rational expression.

Some tutorials:

http://www.youtube.com/watch?v=YbuFd_jio28 Finding LCD (whole numbers)

MAT135

In-Class Assignment

35

http://www.youtube.com/watch?v=omv7Di2o8-Y Adding Rational Expressions

http://www.youtube.com/watch?v=FZdt73khrxA Adding/Subtracting Rational Expressions

Section 6.5 Division of Polynomials

1. Divide as indicated:

4 3 6 5 4

4

2 3 2 3 3 4 4 5

2 3

2 2

12 15 9 3 2) )

3 3

20 4 6 18 9) )

8 6

2 7 10 2) )

2

m m y y ya b

m y

a b ab x y x y x yc d

ab x y

x x x xe f

x x

2

2

4 2

3

)(56 23 2) (8 1)

)( 6 40) ( 10)

)( 25) ( 5)

g x x x

h x x x

i x x

2. Find ( )

( )

f x

g x:

2

4

3

) ( ) 5 24; ( ) 8

) ( ) 16; ( ) 2

) ( ) 8; ( ) 2

a f x x x g x x

b f x y g x y

c f x x g x x

3. To find the average cost of producing an item, divide the total cost by the number of

items produced. A company that manufactures computer disks uses the function

C(x)=200+2x to represent the cost of producing x disks.

a) Find the average cost.

b) What happens to the average cost as more items are produced? Hint: Set up a table.

4. Given 3 2( ) 3 12 5 8P x x x x ,

a) Evaluate ( 6)P

b) Divide 3 23 12 5 8 6x x x x .

c) Compare the value found in (a) to the remainder found in (b). What do you notice?

MAT135

In-Class Assignment

36

d) Evaluate (3)P if 3 2( ) 6 3 5P x x x x and then divide P(x) by 3x . Can you state

a rule that seems to work? This is called the Remainder Theorem.

Section 6.6-6.7 Solving Equations Involving Rational Expressions

and Applications

1. Solve: 8 1

= 302x x

.

17 1. 4 , 0 . , 0, 2 . , 0 . 2

30 4a x b x x c x d

2. Solve: 8 1 2

+4 4 4 1x x

.

. 1,4 , 1, 4 . 1 , 4 . , 1 . 1 , 1a x x b x c x d x

3. Solve: 2 2 2

5 5 5

5 4 8 16 5 4

x x

x x x x x x.

. 7 . 35 . 10 . 7a b c d

4. Find all values of x that satisfy 2

9 5 6( ) , ( ) , ( )

5 5 25f x g x h x

x x x and

= ( )f g x h x .

. 8 . 19 . 76 . 19a b c d

5. The function 22,000 210

( )x

f xx

models the average cost per unit, f(x), for

Electrostuff to manufacture x units of Electrogadget IV. How many units must the

company produce to have an average cost per unit of $400? (Round to the nearest unit.)

.116 units .111 units .117 units .105 unitsa b c d

6. At a warehouse, it takes two employees 1

13

hours to load a truck when they work

together. If it takes one employee working alone 3 hours to load a truck, how long does it

take the other employee working alone?

MAT135

In-Class Assignment

37

Section 6.6-6.7 Solving Equations Involving Rational Expressions

and Applications (continued)

7. Solve the following equations:

2 2 2

2

5 2 1 2 2) ) 2

2 12 3 3

2 4 2 6) ) 0

3 9 3 1

1 1)

2 3 3 1

xa b

x x x x

x yc d

x x x y y y

n ne

n n n n

8. If 4

( )1

f xx

, find all values for which f(x)=3.

9. a. Solve for 1 1 2 22

1 2

: pV p V

VT T

.

b. Solve for y: 1

2

A B

y y .

10. If 2

1 3( ) and ( )

1 1f t g t

t t, find all values for which f(t)=g(t).

11. The shadow cast by a yardstick is 2 ft. long. The shadow cast by a tree is 11 ft. long.

Find the height of the tree.

12. One construction crew can pave a road in 24 hours, and a second crew can do the same

job in 18 hours. How long would it take the two crews working together?

MAT135

In-Class Assignment

38

Sec. 7.1 Radicals Some tutorials:

http://www.algebra.com/algebra/homework/Radicals/Simplifying-Radicals.lesson

http://teachers.henrico.k12.va.us/math/HCPSAlgebra1/Documents/11-

2/SimplifyRadicals.ppt#18

1. Simplify: 55 .

.5 11 .11 5 . 55 .11a b c d

2. Simplify: 2243x .

2 2.9 3 .9 3 .9 3 .9 3a x b x c d x

3. Simplify: 2( 6)

. 6 .6 .36 .not a real numbera b c d

4. Simplify: 64

49.

8 8 8. . .1 .

7 7 7a b c d

5. Simplify: 31

216

3

1 1 1. . . .66 366

a b c d

6. True or false: 3 64 4 .

7. True or false: 18

63

.

8. True or false: 21

73

.

9. What is the domain of ( ) 3 2f x x ? State the answer in interval notation.

MAT135

In-Class Assignment

39

10. What is the domain of 3 2 7x ? State the answer in interval notation

Sec. 7.1 Radicals (continued)

11. Write each of the expressions in simplified form:

a. 3 24 e. 49

100

b. 27 f. 54

6

xy

y

c. 4 73 40x y g. 4

4

81

v

u

d. 2 3 548a b c h. 2

55 1032

p

q r

12. Find the value of each root:

3) 144 ) 100 ) 0.04 ) 27a b c d

MAT135

In-Class Assignment

40

Sec. 7.2 Rational Exponents

1. Simplify each expression:

121

5

34

5 5 2 5

4

564

1052

3

411

3 324

3

4

81)32 )

25

16)( ) )

81

)( ) )7

)( 81) )

a b

c x y dy

pe t f

p

s tg h

w

31

4 2 4 6 21

) ) 2516

i j x y z

2. Simplify a) 2 16 64x x b) 2 6 9x x

3. Write as a single radical: 3 x .

4. The radius of a sphere of volume, V, is given by

1

33

4

Vr . Find the radius of a sphere

having a volume of 85 in.3 (Round to the nearest 0.1 in.)

5. The geometric mean is a statistic used in business and economics. The geometric mean

of three numbers is given by the expression 3 p , where p is the product of the three

numbers. Find the geometric mean of 9, 3, and 8.

MAT135

In-Class Assignment

41

Sec. 7.3 Adding, Subtracting, and Multiplying Radicals

1. Combine the following expressions, if possible. Assume that any variables under

an even root are nonnegative.

a. 4 3 2 3 f. 4 2 23 37x y x xy

b. 6 2y a y a g. 38 6 2 832 3 8x y y x

c. 5 6 3 6 2 6x x x h. 2 3 55 27 6 12a ab b a b

d. 3 35 16 4 54 i. 3 36 327 4 64r r r

e. 35 2y y j. 1 1

128 2252 3

2. Find ( ) ( ) and ( ) ( )f x g x f x g x :

a. 3 3( ) 81 and ( ) 75f x g x

b. 3 2 5( ) 20 and ( ) 45f x a b g x a

3. The ramp shown at the right has a base, b, of 8 feet and a height, h, of 4 feet. The length

of the ramp is given by 2 2b h . Find the length of the ramp.

4. True or false:

a. 4 4 8

b. 12 6 3 8 3

c. 9 4 9 4 5

d. 4 4 4 8 7x x x

MAT135

In-Class Assignment

42

Sec. 7.3 Adding, Subtracting, and Multiplying Radicals

(continued)

5. Multiply or divide as indicated and simplify. Assume that any variables under an even

root are nonnegative.

a. 2 3 5 7

b. 3 33 3 6 9

c. 5 3x x

d. 2

3x

e. 2

2 3a b

f. 7 7v v

g. 5 5v v

6. Find the areas of the figures below:

a. b.

6 2m 40 .ft

10 32m

3 2 .ft

MAT135

In-Class Assignment

43

Sec. 7.4 Quotients, Powers, and Rationalizing Denominators

1. Rationalize the denominator: 121

6.

A. 11 6 B. 11 6

6 C.

121 6

6 D. 47

2. Rationalize the denominator: 3

17 3.

A. 51 3 3

8 B.

51 3 3

20 C.

3 51 17 51

3 D.

51 3 3

8

3. Rationalize the denominator: 6

5 11.

A. 5 11 B. 11 5 C. 6 D. 11 5

4. Simplify:

44

124

256x

y.

A. 3

4

y B.

3

x

y C.

12

4x

y D.

3

4x

y

5. Rationalize the denominator and simplify: 5

4 3x.

A. 5

4 3x B.

20 5 3

16 3

x

x C.

20 5 3

16 3

x

x D.

20 5 3

16 9

x

x

6. Given the area of a circle, the formula A

r can be used to calculate the radius of

the circle. Rewrite the formula.

A. r A B. 2

Ar C.

Ar D.

Ar

A

7. Simplify:

MAT135

In-Class Assignment

44

3 343 34

73 3

. 3 3 . 3 . 3

3 20 50. 27 3 . .

2 10

a b x c x

xd x x e f

z

Sec. 7.5 Solving Equations with Radicals and Exponents

1. Solve: 2 44 2 4 1x x .

A) 4, 12 B) 4,12 C) 2,18 D) 2,18

2. Solve: 3 7 10z .

3. Solve the following problem:

4. Solve: 7 18x x .

A) B) 3 C) 2,9 D) 9

5. Solve for : 2A

r

6. Solve and check each equation.

a. 1 1x x b. 2 2 12 6x x c. 3 9x x

7. Solve and check each equation.

a. 5

38 24 0x b. 2

31 3x c. 4 81x

MAT135

In-Class Assignment

45

8. An airline’s cost for x thousand passengers to travel round trip from New York to

Atlanta is given by ( ) 0.3 1C x x , where ( )C x is measured in millions of

dollars and 0x . Find the airline’s cost for 10,000 passengers. If the airline

charges $320 per passenger, find the profit made by the airline for flying 10,000

passengers from New York to Atlanta.

Sec. 7.6 Complex Numbers

1. Simplify the following as much as possible:

) 36 ) 49 ) 48 ) 12

9 24 9) 65 ) ) )

49 49 4

) 72 ) 6 48

a b c d

e f g h

i j

2. Perform the addition or subtraction and write the result in standard form.

a. 2 18 5 2 b. 7 2 4 36 5i

3. Perform the operation and write the result in standard form.

a. 3 2 5 6i i b. 2

2 4 c. 3 7 2 8

4. Write the quotient in standard form.

a. 4

1 i b.

7 2

2

i

i c.

2

6

3 4

i

i

5. Solve:

a. 2 18x b. 28 24 0x c. 22 72 0x

6. True or false:

a. Every real number is also a complex number.

b. Every complex number is also a real number.

c. 3i i

d. 18 1i

e. 12 9i i i

f. The complex conjugate of 6 2i is 2 6i .

g. The complex conjugate of 10i is 10i .

MAT135

In-Class Assignment

46

7. Show that 2x i is a solution to the equation 2 4 5 0x x .

Sec. 8.1 Factoring and Completing the Square

Tutorials:

http://www.youtube.com/watch?v=_GBtlR4m67g

http://www.youtube.com/watch?v=GyCuj1hx_zc&feature=fvw

1. Solve: 2 18x

A. 3 2x B. 2 3x C. 324 D. 9x

2. Solve: 26 2 386x .

A. 9,9 B. 8 C. 193 D. 8,8

3. Solve: 2 8 16 13x x .

A. 13x B. 9x C. 4 13x D. 4 13x

4. Solve 21 for

3A r r .

A. 3r A B. 3

rA

C. 3A

r D. 3

Ar

5. What must be added to 2 16x x to complete the square?

A. 0 B. 64 C. 64 D. none of these

6. What must be added to 2 2

3x x to complete the square?

A. 1

9 B. 9 C. 0 D. 9

MAT135

In-Class Assignment

47

Sec. 8.1 Factoring and Completing the Square

(continued)

.

MAT135

In-Class Assignment

48

13. Given ( ) and ( )f x g x , find all values for which f(x)=g(x):

a) 2( ) 2 +7x; ( ) 6 8f x x g x x

b) 2( ) 3 ; ( ) 15f x x x g x x

Sec. 8.1 Factoring and Completing the Square

(continued)

14. Solve by completing the square:

2

2

2

2

2

2

2

) 2 8 0

) 4 3 0

)3 9 12 0

) 7 3 0

)3 6 1

)2 4 8 0

)4 3 5 0

a x x

b x x

c x x

d m m

e t t

f x x

g x x

15. A rectangle is 4 feet longer than it is wide, and its area is 20 square feet. Find the

dimensions of the rectangle, to the nearest tenth of a foot.

16. If the lengths of the shorter sides of a right triangle are both x, find the length of the

hypotenuse, in terms of x. What are the measures of the angles in this triangle?

x

x

MAT135

In-Class Assignment

49

Sec. 8.2-8.3 The Quadratic Formula

1. Solve using the quadratic formula:

2

2

2

2

2

2

2

)3 4 2 0

)3 6 2 0

2 1)

4 5 10

) 4 1 0

)2 3

) 10 18

5)

3 6 3

a x x

b x x

r rc

d m m

e t t t

f x x

x x xg

2. Use the discriminant to determine the number and types of solutions for each of the

following equations: 2

2

2

2

2

)2 4 3

)2 1 6

5) 1

2 2

) 6 10 0

)3 6 1

a x x

b x x

r rc

d x x

e t t

3. A woman invests $1,000 in a fund. Interest is compounded annually at a rate r. After

one year, she deposits an additional $2,000. After two years, the balance in the account is

$3,368.10. This is calculated as follows:

23,368.10 1,000(1 ) 2,000(1 )r r

Find the rate, r.

MAT135

In-Class Assignment

50

4. One number is 6 less than another. The product of the numbers is 72. Find the

numbers.

Sec. 8.2-8.3 The Quadratic Formula (continued)

1. Solve: 2

2 8 25x .

A. 13 13

,2 2

B. 3

,02

C. 17

2 D.

3 13,

2 2

2. Solve: 2 18 62 0x x

A. 9 19 B. 9 62 C. 9 19 D. 18 62

3. Solve: 2 6 18 0x x

A. 6,0 B. 3 3i C. 3 9i D. 3 3i

4. The revenue for a small company can be modeled by the quadratic function 2( ) 6 5 340f x x x , where x is the number of years since 1998 and f(x) is in thousands

of dollars. If this trend continues, find the year in which the company’s revenue will be

586 thousand dollars.

A. 2005 B. 2010 C. 2006 D. 2004

5. Use the discriminant to determine the number and type of solution(s) to 2 3 2 0x x .

A. Two complex solutions

B. Two real solutions

C. One real solution

D. It cannot be determined from the given information.

6. The demand equation for a certain product is 45 0.0004P x , where x is the number

of units sold per week and P is the price in dollars ay which one unit is sold. The weekly

revenue, R, is given by R xP . What number of units sold produces a weekly revenue of

$90,000?

A. 110,463 B. 1,733 C. 2,602 D. 8,648

MAT135

In-Class Assignment

51

Sec. 8.2-8.3 The Quadratic Formula (continued)

For numbers 7-9, write a quadratic equation that has the given numbers as solutions.

7. 2, 10x x

A. 2 20 12 0x x B.

2 12 20 0x x

C. 2 20 12 0x x D.

2 12 20 0x x

8. 8x is the only solution.

A. 2 16 64 0x x B.

2 8 64 0x x

C. 2 16 64 0x x D.

2 64 0x

9. 9 8

,4 5

x x

A. 2 77

5 18 04

x x B. 25 72 32 0x x

C. 25 32 72 0x x D.

2 775 18 0

4x x

10. Ron takes two hours more time than Paul to mow the lawn. Working together, they

can mow the lawn in 5 hours. How long does it take each of them working alone?

A. Paul: 10 hours Ron: 12 hours B. Paul: 8.3 hours Ron: 10.3

C. Paul: 9.1 hours Ron: 11.1 hours hours D. Paul: 8 hours Ron: 10 hours

11. Solve: 1 1 1

11 12x x.

A. 13 697

2 B.

35 697

2 C.

13 697

2 D.

35 697

2

12. Find two real numbers that have a sum of 8 and a product of 12.

MAT135

In-Class Assignment

52

Sec. 8.4 Quadratic Functions and Their Graphs

1. Answer the following questions for the graph of

y=f(x) shown at the right:

a) What are the x-intercepts of the graph?

b) What is the y-intercept?

c) ( 2)f

d) What is the vertex?

e) What is the domain and range?

f) Write a possible equation for y=f(x).

g) What is the minimum value of y=f(x)?

2. Answer the following questions for the

graph of y=f(x) shown at the right:

a) What are the x-intercepts of the graph?

b) What is the y-intercept?

c) ( 3)f

d) What is the vertex (approx.)?

e) What is the domain and range?

f) Write a possible equation for y=f(x).

Find the vertex again. Compare with

The answer in (d).

g) What is the maximum value of y=f(x)?

x

y

x

y

MAT135

In-Class Assignment

53

Sec. 8.4 Quadratic Functions and Their Graphs

(continued)

3. For the following functions, find the x-intercepts, y-intercept, vertex, domain and range,

determine if the graph opens upward or downward, and find any maximum or minimum

values. A sketch of the graph is helpful.

2 2

2 2

) 6 5 ) 4 4

) ( ) 2 4 ) ( ) 4 12 9

a y x x b y x x

c f x x x d f x x x

Determine if the given quadratic has a maximum or minimum and then find the

coordinates of that point.

MAT135

In-Class Assignment

54

Sec. 9.1 Graphs of Functions and Relations

1. a. Does Y1 pass through the origin?

b. What is the x-intercept of Y2?

c. For which values of x is Y1=Y2?

d. The graph of Y2 is in which quadrants?

e. The graph of Y1 is in which quadrants?

f. Are both Y1 and Y2 functions?

2. Determine whether the relation is a function. Identify the domain and the range.

a. 3,1 , 5,1 , 7,1 b. 5,0 , 3, 1 , 0,0 , 5, 1 , 3, 2

3. Match the function with the correct graph:

I.2 3 -1

( )3 1

x xf x

x x II

2

2 -1( )

1

xf x

x x III

2

4 2

( ) 2 2

6 2

x

f x x x

x x

A. B.

C.

X Y1 Y2

-3 -5 - 9

-2 - 4 - 4

-1 - 3 - 1

0 - 2 0

1 - 1 - 1

2 0 - 4

3 1 - 9

x

y

y

y

x

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Sec. 9.1 Graphs of Functions and Relations

(continued)

3. Given the piecewise function2

2, if 1( )

1 0, if 1

x xf x

x x , find:

a. (0)f b. ( 1)f c. (3)f d. ( 2)f e. (1)f

4. Graph each function and give its domain and range in interval notation:

2

) ( ) 3 1 ) ( ) +2

) ( ) 3 ) ( ) 2

) ( ) 3 2 ) ( ) 5

a f x x b g x x

c f x x d g x

e h x x f f x x

5. The graph at the right is the graph of

( ) 2 1 4f x x .

a. ( 1)f

b. (3)f

c. ( 2)f

d. ( 3)f

e. For what value(s) is f(x)=2?

f. Why is f(x) a function?

g. Where is the function increasing?

h. Where is the function decreasing?

i. Where is the function constant?

j. From your answers to (a) to (d)

above, list four ordered pairs on the graph of f(x).

x

x

y

x

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Sec. 9.2 Transformation of Graphs

1. Finish the following statements:

a. Suppose you know the graph of ( )y f x and you want to graph ( ) ( )g x af x ,

where a is a positive constant. Then the graph of ( )g x is exactly the same as the graph of

( )f x , but

b. Suppose you know the graph of ( )y f x and you want to graph ( ) ( )g x f x b ,

where b is a negative constant. Then the graph of ( )g x is exactly the same as the graph

of ( )f x , but

c. Suppose you know the graph of ( )y f x and you want to graph ( ) ( )g x f x h ,

where h is a negative constant. Then the graph of ( )g x is exactly the same as the graph

of ( )f x , but

2. The graph of ( )y f x is shown below. Draw the graph of

( ) ( 2) and ( ) ( 3)g x f x h x f x . Don’t forget to label your axes.

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Sec. 9.2 Transformation of Graphs (continued)

3. Name the graphs below.

a. b.

4. Given the graph of g(x) below, draw ( ) ( 2) 1.f x g x Label your axes.

y

x x

y

x

y

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Sec. 9.2 Transformation of Graphs (continued)

5. Without using the graphing calculator, match the graphs with the functions.

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Sec. 10.4 Graphs of Polynomial Functions

1. . Use the graphs to answer the questions that follow. Note the scales on the axes.

a. Which is larger, (0)f or (0)g ?

b. Which is larger, ( 3)f or ( 3)g ?

c. For what value(s), approximately, is ( ) ( )f x g x ?

d. For what value(s) can you say that f(x) =0?

e. What is the behavior of f(x) at its x-intercepts?

f. Explain why both of these graphs represent functions.

y=f(x)

y=g(x)

x

y

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g. What is the y-intercept of f(x)? Of g(x)?

h. Give the domain and range, in interval notation, of both functions.

i. Discuss any symmetry in these functions.

j. On what interval(s) does f(x) increase?

k. On what interval(s) does g(x) increase?

Sec. 10.4 Graphs of Polynomial Functions (continued)

2. Consider the graphs shown below.

a. Fill in the table below.

x f(x) g(x)

0

2

4

x

y=f(x)

y=g(x)

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6

8

10

b. Explain why y=g(x) is not symmetric around the y-axis or around the origin.

c. Find the equation of y=g(x). Could this function have symmetry around the origin or

around the y-axis?

Sec. 10.4 Graphs of Polynomial Functions (continued)

3. Match the graph with the polynomial.

a. b.

c.

d.

I. 3 24 2x x x

x

y

x

y

y

x x

y

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II. 2 3x

III. 3 23x x

IV. 4 23x x

Some problems in this packet have been taken from or adapted from the following texts:

Akst and Bragg, Introductory Algebra Through Applications, Seventh Edition

Akst and Bragg, Intermediate Algebra Through Applications, Second Edition

McKeague, Charles, Intermediate Algebra, Seventh Edition.

Tussy and Gustafson, Elementary and Intermediate Algebra, Third Edition

Stewart, Redlin, Watson, College Algebra, Fourth Edition

Blitzer, College Algebra: An Early Functions Approach, First Edition

Miller, O’Neill, Hyde, Intermediate Algebra, Second Edition