Chapter 2 Test Form A Name Ratti & McWaters, Precalculus ...aplustestbank.eu/sample/Test-Bank-for-Precalculus... · Ratti & McWaters, Precalculus: A Unit Circle Approach, 2e 24 10)

Chapter 2 Test Form A Name Ratti & McWaters, Precalculus: A Unit Circle Approach, 2e

1) For ( ) ( )( ) ( )4 63 27 2 5 16 5f x x x x x= − + + , determine: a) the real roots,

b) their multiplicity, and c) whether the graph crosses or touches the x-axis at each root. 1)

2) For the following polynomial use Descartes’s rule of signs to determine the

possible number of positive and negative rational roots.

5 4 3 23 5 15 4 12x x x x x− − + + − 2)

3) List all the possible rational roots of 3 22 3 29 60x x x− − + and factor the polynomial. 3)

4) Use the given roots to factor 5 4 3 22 9 9 3 7 6x x x x x+ + + + − .

, 2x i= − 4)

5) Find the equation in standard form of the parabolic function that passes through ( )1,27 with vertex at ( )3, 5− − . 5)

6) Sketch the graph of ( ) 3 22 11 12f x x x x= − − + .

State the x- and y-intercepts.

6)

7) Determine the end behavior for ( ) ( ) ( )3 52 1 3 .f x x x x=− − + 7)

8) y varies directly with 2 ,x and 8

5y = when 2.x = Find the value of ,k

write the equation that represents this variation, and find the value of y

when 3.x = 8)

9) Find the equation of the oblique asymptote for

( )3 2

2

2 9 10 29

3 10

x x xf x

x x

− − +=

− −

9)

23

http://www.parmispdf.com

Chapter 2 Test Form A Name Ratti & McWaters, Precalculus: A Unit Circle Approach, 2e

24

10) Given ( ) 24 52 21f x x x=− + + , determine: a) if function has a maximum

or minimum value, b) where this value occurs, and c) what that value is. 10)

In exercises 11–12, graph the rational function. List all intercepts and asymptotes.

11) ( )2

2

2 5 3

25

x xf x

x

+ −=

−

11)

12) ( )2

3

2 15

xf x

x x

−=

− −

12)

13) z varies directly with x and inversely with ,y and 43.75z = when

25x = and 0.2.y = Find z when 20x = and 0.4.y = 13)

14) The cost, in dollars, to produce x items is given by 20 400.C x= + If the demand function is given by 500 10 ,p x= − find the value of x that

maximizes profit and state that maximum profit. 14)

15) The sum of two numbers is 90. Determine if the numbers have a maximum or minimum product and find that product.

15)


Chapter 2 Test Form B Name Ratti & McWaters, Precalculus: A Unit Circle Approach, 2e

1) For ( ) ( ) ( ) ( )532 25 3 2 9 4f x x x x x=− + + − , determine: a) the real roots,

b) their multiplicity, c) whether the graph crosses or touches the x-axis at each root, and d) the end behavior of the graph. 1)



5 4 3 23 5 15 4 12x x x x x+ − − + + 2)

3) List all the possible rational roots of 3 23 5 88 60x x x− − + and factor the polynomial. 3)

4) Use the given roots to factor 5 4 3 23 4 5 10 68 24x x x x x− − − − + .

2 ,3x i= 4)

5) Find the equation in standard form of the parabolic function that passes through ( )4, 5− − with vertex at ( )2,7− . 5)

6) Sketch the graph of ( ) 3 22 29 30f x x x x= + − − .


6)

7) Determine the end behavior for ( ) ( ) ( )6 34 7 .f x x x x= + − 7)

8) y varies directly with 3,x and 135

4y =− when 3.x =− Find the value

of ,k write the equation that represents this variation, and find the value of y when 5.x = 8)


( )3 2

2

4 11 18 37

6

x x xf x

x x

− + + −=

− −

9)

25


Chapter 2 Test Form B Name Ratti & McWaters, Precalculus: A Unit Circle Approach, 2e

26

10) Given ( ) 26 38 14f x x x= + − determine: a) if function has a maximum or

minimum value, b) where this value occurs, and c) what that value is. 10)


11) ( )2

2

9 3 2

16

x xf x

x

− −=

−

11)

12) ( )2

3

2 15

xf x

x x

+=

+ −

12)

13) z varies directly with x and inversely with ,y and 16z = when 12x =

and 1.2.y = Find z when 9x = and 1.5.y = 13)



15) The difference of two numbers is 110. Determine if the numbers have a maximum or minimum product and find that product.

15)


Chapter 2 Test Form C Name Ratti & McWaters, Precalculus: A Unit Circle Approach, 2e

1) For ( ) ( )( ) ( )2 74 24 4 5 4 3f x x x x x= − + − , determine: a) the real roots,




5 4 3 27 15 5 16 12x x x x x− + − − + 2)

3) List all the possible rational roots of 3 22 54 72x x x− − − and factor the polynomial. 3)

4) Use the given roots to factor 5 4 3 25 12 6 6 11 6x x x x x− − − − + .

,3x i=− 4)

5) Find the equation in standard form of the parabolic function that passes through ( )4, 6− with vertex at ( )5, 8− . 5)

6) Sketch the graph of ( ) 3 23 22 24f x x x x= − − + .


6)

7) Determine the end behavior for ( ) ( ) ( )6 23 4 7 .f x x x x=− − + 7)

8) y varies directly with 2 ,x and 48



when 2.x = 8)


( )3 2

2

3 14 14 47

3 10

x x xf x

x x

− − +=

− −

9)

27


Chapter 2 Test Form C Name Ratti & McWaters, Precalculus: A Unit Circle Approach, 2e

28

10) Given ( ) 24 70 91f x x x= + − determine: a) if function has a maximum or

minimum value, b) where this value occurs, and c) what that value is. 10)


11) ( )2

2

2 7 4

25

x xf x

x

− −=

−

11)

12) ( )2

2

20

xf x

x x

+=

− −

12)


2.3x = and 7.y = Find z when 1.4x = and 4.y = 13)



15) The sum of two numbers is 70. Determine if the numbers have a maximum or minimum product and find that product.

15)


Chapter 2 Test Form D Name Ratti & McWaters, Precalculus: A Unit Circle Approach, 2e

1) For ( ) ( ) ( ) ( )34 523 5 2 1 6f x x x x x=− − + − , determine: a) the real roots,




5 4 3 29 20 12x x x x x− − + + + 2)

3) List all the possible rational roots of 3 23 28 52 48x x x− + + and factor the polynomial. 3)

4) Use the given roots to factor 5 4 3 24 21 30 60 56 96x x x x x− + − + + .

2 ,4x i=− 4)

5) Find the equation in standard form of the parabolic function that passes through ( )3,5 with vertex at ( )4,7 . 5)

6) Sketch the graph of ( ) 3 22 19 20f x x x x= − − +


6)

7) Determine the end behavior for ( ) ( ) ( )2 34 3 2 .f x x x x= − + 7)

8) y varies directly with 3,x and 45



when 4.x = 8)


( )3 2

2

2 81 177

2 35

x x xf x

x x

− + + −=

+ −

9)

29


Chapter 2 Test Form D Name Ratti & McWaters, Precalculus: A Unit Circle Approach, 2e

30

10) Given ( ) 28 84 50f x x x=− + − determine: a) if function has a maximum

or minimum value, b) where this value occurs, and c) what that value is. 10)


11) ( )2

2

5 3 2

9

x xf x

x

+ −=

−

11)

12) ( )2

4

4 12

xf x

x x

+=

+ −

12)


1.1x = and 14.y = Find z when 2.3x = and 2.y = 13)



15) The difference of two numbers is 120. Determine if the numbers have a maximum or minimum product and find that product.

15)


Chapter 2 Test Form E Name Ratti & McWaters, Precalculus: A Unit Circle Approach, 2e

In exercises 1–2, use ( ) 5 4 3 23 5 27 32 12f x x x x x x= + − − − −

1) What are the possible number of negative rational roots?

a) 3,1 b) 4,2,0 c) 1 d) 2,0

1)

2) What are the possible number of positive rational roots?

a) 3,1 b) 4,2,0 c) 1 d) 2,0

2)

3) Determine the end behavior for ( ) ( )( )53 1 6 .f x x x x=− − +

a) as

as

y x

y x

⎧ →−∞ →−∞⎪⎪⎨⎪ →−∞ →∞⎪⎩ b)

as

as

y x

y x

⎧ →−∞ →−∞⎪⎪⎨⎪ →∞ →∞⎪⎩

c) as

as

y x

y x

⎧ →∞ →−∞⎪⎪⎨⎪ →∞ →∞⎪⎩ d)

as

as

y x

y x

⎧ →∞ →−∞⎪⎪⎨⎪ →−∞ →∞⎪⎩

3)

4) Which of the following is not a possible rational root of 3 25 41 54 72?x x x+ + −

a) 85

b) 53

c) 6 d) 35

−

4)

5) Use the given roots to factor 5 4 3 22 5 13 16 84 144;x x x x x− − + − + 2 ,4x i=−

a) ( )( )( )( )( )3 4 2 3 2 2x x x x i x i+ − − − +

b) ( )( )( )( )( )3 4 2 3 2 2x x x x i x i+ + + − +

c) ( )( )( )( )( )3 4 2 3 2 2x x x x x+ − − − +

d) ( )( )( )( )( )3 4 2 3 2 2x x x x x− + − − +

5)

6) For which root does the graph of ( ) ( ) ( ) ( )64 327 4 5 1 2f x x x x x= − + − touch the x-axis?

a) 0 b) 54

c) 2 d) i−

6)

7) Which root of ( )( ) ( )4 63 27 2 5 16 5x x x x− + + has multiplicity 3?

a) 52

b) 5− c) 0 d) none

7)

8) Which of the following is not the coordinate of an intercept of 3 22 43 40x x x− − − ?

a) ( )5,0− b) ( )8,0− c) ( )1,0− d) ( )0, 40−

8)

9) Determine the coordinates of the minimum of ( ) 210 22 40.f x x x= − +

a) ( )684115 5

,− b) ( )115

,40 c) ( )7631110 10

,− d) ( )2791110 10

,

9)

31



32

10) Determine the equation of the horizontal asymptote for ( )2

2

15 2

21 4

x xf x

x x

− −=

− −

a) 57

y = b) 2y =− c) 2y = d) 2y x=

10)

11) Sketch the graph of ( ) 3 22 43 40f x x x x= − − −

a) b)

c) d)

11)

12) Find the equation, in standard form, of the parabolic function that passes through

( )1,4− with the vertex at ( )3, 4 .− −

a) ( ) ( )22 3 4f x x=− + − b) ( ) ( )22 3 4f x x=− − −

c) ( ) ( )22 3 4f x x= − − d) ( ) ( )22 3 4f x x= + −

12)

13) z varies directly with x and inversely with ,y and 0.42z = when 8x = and 6.y =

Find z when 4x = and 5.y =

a) 0.175 b) 0.252 c) 0.7 d) 1.008

13)



14) Graph ( )2

2

25

6

xf x

x x

−=

+ −.

a) b)

c) d)

14)

15) y varies directly with 2x , and 12

5y = when 9x = . Write the equation that describes

this statement, and find y when 15.x =

a) 216

25

xy = ; 144y = b)

225

16

xy = ;

5625

16y =

c) 2135

4

xy = ;

30375

4y = d)

24

135

xy = ;

20

3y =

15)

16) Find the equation of the oblique asymptote for ( )3 2

2

3 17 31 24

5 14

x x xf x

x x

+ − −=

+ −.

a) 3y x= b) 3 17y x= + c) 3 2y x= + d) 3y =

16)

33



34

17) Graph ( )2

1

4 12

xf x

x x

+=

+ −.

a) b)

c) d)

17)

18) The difference of two numbers is 80. Determine if the numbers have a maximum or

minimum product and find the product.

a) Maximum; 1600 b) Minimum; 1600 c) Maximum; 1600− d) Minimum; 1600−

18)

19) The cost, in dollars, to produce x items is given by 12 120.C x= + If the demand

function is given by 116 4 ,p x= − find the value of x that maximizes profit and state

that maximum profit.

a) 16;x = $1,144 b) 16;x = $904

c) 13;x = $796 d) 13;x = $556

19)


Chapter 2 Test Form F Name Ratti & McWaters, Precalculus: A Unit Circle Approach, 2e

In exercises 1–2, use ( ) 5 4 3 25 3 17 28 12f x x x x x x= − + + − +

1) What are the possible number of negative rational roots?

a) 3,1 b) 4,2,0 c) 1 d) 2,0

1)

2) What are the possible number of positive rational roots?

a) 5,3,1 b) 4,2,0 c) 3,1 d) 2,0

2)

3) Determine the end behavior for ( ) ( ) ( )32 7 6 .f x x x x= − +

a) as

as

y x

y x

⎧ →−∞ →−∞⎪⎪⎨⎪ →−∞ →∞⎪⎩ b)

as

as

y x

y x

⎧ →−∞ →−∞⎪⎪⎨⎪ →∞ →∞⎪⎩

c) as

as

y x

y x

⎧ →∞ →−∞⎪⎪⎨⎪ →∞ →∞⎪⎩ d)

as

as

y x

y x

⎧ →∞ →−∞⎪⎪⎨⎪ →−∞ →∞⎪⎩

3)

4) Which of the following is not a possible rational root of 3 23 13 6 40?x x x+ − −

a) 35

b) 23

− c) 8− d) 53

4)

5) Use the given roots to factor 5 4 3 23 4 14 42 117 54;x x x x x− + − − − 3 , 1x i= −

a) ( )( )( )( )( )3 2 3 1 3 3x x x x i x i− + − − +

b) ( )( )( )( )( )3 2 3 1 3 3x x x x i x i+ − + − +

c) ( )( )( )( )( )3 2 3 1 3 3x x x x x− + − − +

d) ( )( )( )( )( )3 2 3 1 3 3x x x x x+ − + − +

5)

6) For which root does the graph of ( ) ( ) ( ) ( )24 65 23 3 5 4 5f x x x x x= + + + cross the

x-axis?

a) 0 b) 53

− c) 4− d) 2i

6)

7) Which root of ( ) ( )( )5 34 25 4 3 9 4x x x x+ + − has multiplicity 5?

a) 4 b) 34

− c) 0 d) none

7)

8) Which of the following is not the coordinate of an intercept of 3 2 26 24x x x− − − ?

a) ( )4,0 b) ( )1,0− c) ( )6,0 d) ( )0, 24−

8)

9) Determine the coordinates of the minimum of ( ) 26 15 13.f x x x= + +

a) ( )52

,13− b) ( )5 294 8

,− c) ( )52

,88 d) ( )5 3294 8

,

9)

35



36

10) Determine the equation of the horizontal asymptote for ( )2

2

20 7 3

12 4

x xf x

x x

− −=

− −.

a) 3y x= b) 3y = c) 3y =− d) 53

y =

10)

11) Sketch the graph of ( ) 3 23 22 24f x x x x= − − +

a) b)

c) d)

11)

12) Find the equation, in standard form, of the parabolic function that passes through ( )1, 3−

with the vertex at ( )2, 5− .

a) ( ) ( )22 2 5f x x=− + − b) ( ) ( )22 2 5f x x= − −

c) ( ) ( )22 2 5f x x=− − − d) ( ) ( )22 2 5f x x= + −

12)

13) z varies directly with x and inversely with ,y and 0.52z = when 5x = and 8.y =

Find z when 6x = and 4.y =

a) 0.217 b) 0.312 c) 0.693 d) 1.248

13)



14) Graph ( )2

2

16.

6

xf x

x x

−=

− −

a) b)

c) d)

14)

15) y varies directly with 3x , and 30

7y = when 6x = . Write the equation that describes

this statement, and find y when 4.x =

a) 35

252

xy = ;

80

63y = b)

3252

5

xy = ;

16128

5y =

c) 3343

4500

xy = ;

5488

1125y = d)

24500

343

xy = ;

288000

343y =

15)

16) Find the equation of the oblique asymptote for ( )3 2

2

3 4 50 29

2 15

x x xf x

x x

− − + −=

+ −.

a) 3y x=− b) 3 4y x= − c) 3y =− d) 3 2y x=− +

16)

37



38

17) Graph ( )2

1.

12

xf x

x x

−=

+ −

a) b)

c) d)

17)

18) The sum of two numbers is 60. Determine if the numbers have a maximum or minimum

product and find the product.

a) Maximum; 900 b) Minimum; 900 c) Maximum; 900− d) Minimum; 900−

18)

19) The cost, in dollars, to produce x items is given by 16 180.C x= + If the demand

function is given by 400 8 ,p x= − find the value of x that maximizes profit and state

that maximum profit.

a) 24;x = $4,788 b) 24;x = $4,428

c) 26;x = $5,588 d) 26;x = $5,228

19)


Ratti & McWaters, Precalculus: A Unit Circle Approach, 2e Answers Chapter 2 Tests

176

Form A 1) Root Multiplicity Touch or Cross

0 3 Cross

5

2 1 Cross

5− 6 Touch

2) Number of possible positive rational roots: 3, 1

Number of possible negative rational roots: 2, 0

3) 1 3 5 15

, 1, , 2, , 3, 4, 5, 6, , 10, 12, 15, 20, 30, 602 2 2 2

⎧ ⎫⎪ ⎪⎪ ⎪± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±⎨ ⎬⎪ ⎪⎪ ⎪⎩ ⎭;

( )( )( )3 4 2 5x x x− + −

4) ( )( )( )( )( )3 2 1 2x x x x i x i+ − + − + 5) ( ) ( )22 3 5f x x= + −

6)

( ) ( ) ( ) ( )3,0 , 1,0 , 4,0 , 0,12−

7) as and

as

y x

y x

→−∞ →−∞→−∞ →∞

8) 2

5k = ;

22

5

xy = ;

18

5y =

9) 2 3y x= −

10) a) maximum

b) 13

2x =

c) 13

1902

f⎛ ⎞⎟⎜ =⎟⎜ ⎟⎜⎝ ⎠

11)

x-intercept: 12

3,x =−

y-intercept: 325

y =

vertical asymptotes: 5, 5x x=− = horizontal asymptote: 2y =



12)

x-intercept: 3x =

y-intercept: 15

y =


13) 17.5 14) ( )24 $5,360P = 15) Maximum of 2025

Form B 1) Root Multiplicity Touch or Cross

0 2 Touch

2

3− 3 Cross

4 1 Cross

2) Number of possible negative rational roots: 3,1

Number of possible positive rational roots: 2, 0

3) 1 2 4 5 10 20

, 1, , , 2, 3, , 4, 5, 6, , 10, 12, 15, 20, 30, 603 3 3 3 3 3

⎧ ⎫⎪ ⎪⎪ ⎪± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±⎨ ⎬⎪ ⎪⎪ ⎪⎩ ⎭;

( )( )( )5 3 2 6x x x+ − −

4) ( )( )( )( )( )3 3 1 2 2 2x x x x i x i− − + − + 5) ( )2( ) 3 2 7f x x=− + +

6)

( ) ( ) ( ) ( )6,0 , 1,0 , 5,0 , 0, 30− − −

7) as and

as

y x

y x

→∞ →−∞

→∞ →∞

8) 5

4k = ;

35

4

xy = ;

625

4y =

9) 4 7y x=− +

10) a) minimum

b) 19

6x =−

c) 19 445

6 6f⎛ ⎞⎟⎜− =−⎟⎜ ⎟⎜⎝ ⎠

177



178

11)

x-intercepts: 32

3,x =−

y-intercept: 916

y =−

vertical asymptotes: 4, 4x x=− = horizontal asymptote: 2y =−

12)

x-intercept: 3x =−

y-intercept: 15

y =−


13) 9.6 14) ( )50 $9,900P = 15) Minimum of 3025−

Form C 1) Root Multiplicity Touch or Cross

0 4 Touch

5

4 1 Cross

3 7 Cross

2) Number of possible negative rational roots: 1

Number of possible positive rational roots: 4, 2, 0

3) 1 3 9

, 1, , 2, 3, 4, , 6, 8, 9, 12, 18, 24, 36, 722 2 2

⎧ ⎫⎪ ⎪⎪ ⎪± ± ± ± ± ± ± ± ± ± ± ± ± ± ±⎨ ⎬⎪ ⎪⎪ ⎪⎩ ⎭;

( )( )( )6 2 3 4x x x− + +

4) ( )( )( )( )( )3 1 5 2x x x x i x i− + − − + 5) ( )2( ) 2 5 8f x x= − −



6)

( ) ( ) ( ) ( )4,0 , 1,0 , 6,0 , 0, 24−

7) as and

as

y x

y x

→∞ →−∞

→−∞ →∞

8) 3

7k = ;

23

7

xy = ;

12

7y =

9) 3 5y x= −

10) a) minimum

b) 35

4x =−

c) 35 1589

4 4f⎛ ⎞⎟⎜− =−⎟⎜ ⎟⎜⎝ ⎠

11)

x-intercepts: 12

, 4x =−

y-intercept: 425

y =


12)


y-intercept: 110

y =−


13) 0.49 14) ( )37 $6,635P = 15) Maximum of 1225

179



180

Form D 1) Root Multiplicity Touch or Cross

0 1 Cross

2

5 4 Touch

6 5 Cross

2) Number of possible negative rational roots: 3,1

Number of possible positive rational roots: 2, 0

3) 1 2 4 8 16

, , 1, , 2, , 3, 4, , 6, 8, 12, 16, 24, 483 3 3 3 3

⎧ ⎫⎪ ⎪⎪ ⎪± ± ± ± ± ± ± ± ± ± ± ± ± ± ±⎨ ⎬⎪ ⎪⎪ ⎪⎩ ⎭;

( )( )( )6 3 2 4x x x− + −

4) ( )( )( )( )( )4 4 3 2 2 2x x x x i x i− + − − + 5) ( ) ( )22 4 7f x x=− − +

6)

( ) ( ) ( ) ( )4,0 , 1,0 , 5,0 , 0,20−

7) as and

as

y x

y x

→−∞ →−∞

→∞ →∞

8) 5

6k = ;

35

6

xy = ;

160

3y =

9) 2 5y x=− +

10) a) maximum

b) 21

4x =

c) 21 341

4 2f⎛ ⎞⎟⎜ =⎟⎜ ⎟⎜⎝ ⎠

11)

x-intercepts: 52

1,x =−

y-intercept: 59

y =−

vertical asymptotes: 3, 3x x=− = horizontal asymptote: 2y =−



12)


y-intercept: 13

y =−


13) 4.025 14) ( )34 $6,840P = 15) Minimum of 3600−

Form E 1) B 2) C 3) D 4) B 5) A 6) B

7) C 8) B 9) D 10) C 11) C 12) D

13) B 14) C 15) D 16) C 17) D 18) D

19) D

Form F 1) C 2) B 3) C 4) A 5) B 6) A

7) B 8) A 9) B 10) B 11) A 12) B

13) D 14) B 15) A 16) D 17) B 18) A

19) B

181


Documents

Chapter 2 Test Form A Name Ratti & McWaters, Precalculus ...aplustestbank.eu/sample/Test-Bank-for-Precalculus... · Ratti & McWaters, Precalculus: A Unit Circle Approach, 2e 24 10)