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Chapter 2 Test Form A Name Ratti & McWaters, College Algebra and Trigonometry and Precalculus: A Right Triangle Approach, 2e

1) Find the distance and midpoint between ( )5,6− and ( )2, 4 .− 1)

2) Write the equation, in standard form, for the circle graphed below.

2)

3) Find the equation of the line passing through ( )8, 7− that is perpendicular to the

line 10 15 22.x y− = 3)

4) Find the domain of ( )2

10 2.

4 32

xf x

x x

− −=

+ −

4)

5) Given ( )

2 8 if 4

2 4if 4 5,

311 if 5

x x x

xf x x

xx

⎧⎪− + ≤−⎪⎪⎪⎪ +⎪= − < ≤⎨⎪ +⎪⎪⎪ >⎪⎪⎩

evaluate ( ) ( )4 , 5 ,f f− and ( )10 .f 5)

6) State the domain and range of the function graphed below.

6)

31



7) State the x - and y -intercepts of ( ) 2 10 16.f x x x= + + 7)

8) When is the function graphed below increasing or decreasing? What are the coordinates of the relative minimum and maximum of the function?

8)

9) Test 2

34 2

4xy

x y=

+ for symmetry with respect to the x -axis, the y -axis, and

the origin. 9)

10) Given ( )2

2

2 3

30

xf x

x

− +=

− and ( ) 5 10,g x x= + find ( )( )f g x and its

domain. 10)

11) Given the graph of ( ),f x draw the graph of 1

2 .3

f x⎛ ⎞⎟⎜− − ⎟⎜ ⎟⎜⎝ ⎠

11)

12) Find the equation of the circle, in standard form, for 2 210 14 58 0x x y y− + + + = 12)

32



13) Write the formula for the piecewise function graphed below.

13)

14) Find the difference quotient for ( ) 35 .f x x x= − 14)

15) Given ( ) 3 7,

2 8

xf x

x

−=

+ find ( )1f x− and the range of ( ).f x

15)

16) A manufacturing company purchases a milling machine and depreciates its value linearly. The machine is worth $10,200 after 3 years and $9,000 after 5 years. Find a linear equation giving the value, V , of the machine t years after purchase. What was the original value of the machine? When will the machine have no value? 16)

33


Chapter 2 Test Form B Name Ratti & McWaters, College Algebra and Trigonometry and Precalculus: A Right Triangle Approach, 2e

1) Find the distance and midpoint between ( )7, 8− and ( )3,5 .− 1)


2)

3) Find the equation of the line passing through ( )9, 2− − that is perpendicular to

the line 12 20 17.x y+ = 3)


3 12.

56

xf x

x x

+=

+ −

4)

5) Given ( ) 3 2

14if 5

2

2 if 5 3,

6 if 3

xx

x

f x x x x

x

⎧ −⎪⎪ <−⎪⎪ −⎪⎪⎪= − + − ≤ <⎨⎪⎪⎪− ≥⎪⎪⎪⎪⎩

evaluate ( ) ( )8 , 5 ,f f− − and ( )3 .f 5)


6)

34



7) State the x - and y -intercepts of 2 15 36.y x x= − + 7)


8)

9) Test 3

34 2

4xy

x y=

+ for symmetry with respect to the x -axis, the y -axis, and

the origin. 9)

10) Given ( )2

2

7

2 30

xf x

x

− +=


domain. 10)

11) Given the graph of ( ),f x draw the graph of 1 1

.3 2

f x⎛ ⎞⎟⎜− − ⎟⎜ ⎟⎜⎝ ⎠

11)

12) Find the equation of the circle, in standard form, for 2 210 14 58 0x x y y+ + − + = 12)

35




13)

14) Find the difference quotient for ( ) 3 4 .f x x x= − 14)

15) Given ( ) 5 3,

4 8

xf x

x

+=

− find ( )1f x− and the range of ( ).f x

15)

16) A warehouse purchases a forklift and depreciates its value linearly. The forklift is worth $35,000 after 4 years and $22,500 after 9 years. Find a linear equation giving the value, V , of the forklift t years after purchase. What was the original value of the forklift? When will the forklift have no value? 16)

36


Chapter 2 Test Form C Name Ratti & McWaters, College Algebra and Trigonometry and Precalculus: A Right Triangle Approach, 2e

1) Find the distance and midpoint between ( )9,7− and ( )2, 5 .− 1)


2)

3) Find the equation of the line passing through ( )16,9− that is perpendicular to

the line 16 14 23.x y− + = 3)


2 12.

2 35

xf x

x x

+=

+ −

4)

5) Given ( ) 2

13 if 2

9 7 if 2 7 ,

11if 7

1

x

f x x x x

xx

x

⎧⎪⎪⎪ <−⎪⎪⎪⎪= − + + − ≤ <⎨⎪⎪⎪ +⎪ ≥⎪⎪ −⎪⎩

evaluate ( ) ( )10 , 2 ,f f− − and ( )7 .f 5)


6)

37



7) State the x - and y -intercepts of 3 2 64.y x= − 7)


8)

9) Test 4

23

2 5

7

yy

x

+=

− for symmetry with respect to the x -axis, the y -axis, and

the origin. 9)

10) Given ( )2

2

4

2 42

xf x

x

− +=


domain. 10)

11) Given the graph of ( ),f x draw the graph of ( )3 2 .f x− −

11)

12) Find the equation of the circle, in standard form, for 2 212 18 92 0x x y y− + + + = 12)

38




13)

14) Find the difference quotient for ( ) 3 5 .f x x x= − 14)

15) Given ( ) 4 7,

3 12

xf x

x

−=

− find ( )1f x− and the range of ( ).f x

15)

16) A garage purchases a smog testing machine and depreciates its value linearly. The machine is worth $6,050 after 3 years and $4,950 after 5 years. Find a linear equation giving the value, V , of the machine t years after purchase. What was the original value of the milling machine? When will the machine have no value? 16)

39


Chapter 2 Test Form D Name Ratti & McWaters, College Algebra and Trigonometry and Precalculus: A Right Triangle Approach, 2e

1) Find the distance and midpoint between ( )13, 16− and ( )2,8 .− 1)


2)

3) Find the equation of the line passing through ( )12,5 that is perpendicular to the

line 18 30 53.x y+ = 3)


3 15.

4 21

xf x

x x

− +=

− −

4)

5) Given ( )

2 32 if 4

21 if 4 11,

3 5if 11

7

x x x

f x x

xx

x

⎧⎪⎪⎪− − ≤−⎪⎪⎪⎪= − − < ≤⎨⎪⎪⎪ −⎪ >⎪⎪ −⎪⎩

evaluate ( ) ( )4 , 11 ,f f− and ( )15 .f 5)


6)

40



7) State the x - and y -intercepts of 3 2 7 8.y x x= − − 7)


8)

9) Test 4

33

7yx

y x=

− for symmetry with respect to the x -axis, the y -axis, and the

origin. 9)

10) Given ( )2

2

3 5

48

xf x

x

−=

− and ( ) 4 32,g x x= + find ( )( )f g x and its domain.

10)

11) Given the graph of ( ),f x draw the graph of ( )12 .

3f x− −

11)

12) Find the equation of the circle, in standard form, for 2 220 6 60 0x x y y+ + − + = 12)

41




13)

14) Find the difference quotient for ( ) 37 .f x x x= − 14)

15) Given ( ) 7 6,

5 15

xf x

x

+=

+ find ( )1f x− and the range of ( ).f x

15)

16) A publisher purchases a printing press and depreciates its value linearly. The printing press is worth $14,250 after 5 years and $8,250 after 13 years. Find a linear equation giving the value, V , of the printing press t years after purchase. What was the original value of the printing press? When will the printing press have no value? 16)

42


Chapter 2 Test Form E Name Ratti & McWaters, College Algebra and Trigonometry and Precalculus: A Right Triangle Approach, 2e

For Exercises 1–2, use the points ( )6,7− and ( )2, 4 .−

1) Find the distance between the points.

a) 185 b) 5 c) 133 d) 7

1)

2) Find the midpoint between the points.

a) 11

4,2

⎛ ⎞⎟⎜ − ⎟⎜ ⎟⎜⎝ ⎠ b)

32,

2

⎛ ⎞⎟⎜ − ⎟⎜ ⎟⎜⎝ ⎠ c)

114,

2

⎛ ⎞⎟⎜− ⎟⎜ ⎟⎜⎝ ⎠ d)

32,

2

⎛ ⎞⎟⎜− ⎟⎜ ⎟⎜⎝ ⎠

2)

3) Write the equation, in standard form, for the

circle graphed to the right.

a) ( ) ( )2 22 3 36x y− + − =

b) ( ) ( )2 22 3 36x y+ + + =

c) ( ) ( )2 22 3 6x y− + − =

d) ( ) ( )2 22 3 6x y+ + + =

3)

4) Find the equation of the line passing through ( )12, 7− that is perpendicular to the line

14 21 17.x y− + =−

a) 3

252

y x= − b) 3

112

y x=− + c) 2

153

y x= − d) 2

13

y x= +

4)


3 15.

4 21

xf x

x x

− +=

− −

a) ( ) ( ], 3 3,5−∞ − ∪ − b) ( ],5−∞

c) [ )5,−∞ d) [ ) ( )5,7 7,∪ ∞

5)

6) State the x - and y - intercepts of 2 15 36.y x x= + +

a) ( )( ) ( )0, 3 0, 12 , 6,0− − b) ( )( ) ( )3,0 12,0 , 0,6− −

c) ( )( ) ( )0, 3 0, 12 , 36,0− − d) ( )( ) ( )0, 3 0, 12 , 36,0− −

6)

43



For Exercises 7–9, use ( )

2 32 if 5

3 5if 5 9.

78 if 9

x x x

xf x x

xx

⎧⎪− − ≤−⎪⎪⎪⎪ −⎪= − < ≤⎨⎪ −⎪⎪⎪− >⎪⎪⎩

7) Find ( )5 .f −

a) 11− b) 225 c) 5

3− d) 275−

7)

8) Find ( )9 .f

a) 1539− b) 8− c) 121

7 d) 11−

8)

9) Find ( )11 .f

a) 2783− b) 8− c) 7− d) 149

7

9)

For Exercises 10–11, use the graph to the right.

10) State the domain of the function.

a) [ ) [ )10, 4 1,− − ∪ − ∞

b) [ ] [ )6, 2 4,− ∪ ∞

c) ( ] ( )10, 4 1,− − ∪ − ∞

d) ( ) ( )6,2 4,− ∪ ∞

11) State the range of the function. a) ( ),−∞ ∞

b) ( ] [ )4, 2 4,− ∪ ∞

c) [ ] [ )6, 2 4,− ∪ ∞

d) [ ) [ )10, 4 1,− − ∪ − ∞

10) 11)

12) Find the equation of the circle, in standard form, for 2 210 8 23 0.x x y y− + + − =

a) ( ) ( )2 25 4 64x y− + + = b) ( ) ( )2 2

10 8 23x y− + + =

c) ( ) ( )2 25 4 64x y+ + + = d) ( ) ( )2 2

5 4 8x y− + + =

12)

44




13) When is the function increasing or decreasing?

a) Decreasing( ) ( ), 5 4, ;−∞ − ∪ ∞

Increasing: ( )5,4−

b) Decreasing: ( )5,4−

Increasing: ( ) ( ), 5 4, ;−∞ − ∪ ∞

c) Decreasing: ( )7,5 ;−

Increasing: ( ) ( ), 7 5,−∞ − ∪ ∞

d) Decreasing: ( ) ( ), 7 5, ;−∞ − ∪ ∞

Increasing: ( )7,5 ;−

14) What are the coordinates of the relative

minimum of the function? a) ( )8,8− b) ( )4,6−

c) ( )3, 7− d) ( )7,10


maximum of the function? a) ( )8,8− b) ( )4,6−

c) ( )3, 7− d) ( )7,10

13) 14) 15)

16) Test 3

25 2

2yx

x y=

− for symmetry with respect to the x -axis, the y -axis, and the origin.

a) x axis b) y axis c) origin d) no symmetry

16)

For Exercises 17–18 use ( )2

2

5 10

30

xf x

x

− +=

− and ( ) 22 2 .g x x= −

17) Find ( )( ).f g x

a) ( )( )2

2

32 674

30

xf g x

x

−=

− b) ( )( ) 5 60

4

xf g x

x

+=

−

c) ( )( ) 5 50

4

xf g x

x

− +=

+ d) ( )( ) 5 60

4

xf g x

x

−=

+

17)

18) What is the domain of ( )( )?f g x

a) [ ) ( )11, 4 4,− − ∪ − ∞ b) [ )11,− ∞

c) ( ]4,11− d) ( ) ( ], 4 4,11−∞ − ∪ −

18)

45



19) Given the graph of ( ),f x draw the graph of 1 1

.3 2

f x⎛ ⎞⎟⎜− ⎟⎜ ⎟⎜⎝ ⎠

a) b)

c)

d)

19)

46



20) Write the formula for the piecewise function graphed to the right.

a) ( )5 if 3

3 5 7 if 3

xf x

x x

⎧ ≤⎪⎪=⎨⎪ − − >⎪⎩

b) ( )5 if 3

3 5 7 if 3

xf x

x x

⎧ ≤⎪⎪=⎨⎪ + − >⎪⎩

c) ( )5 if 3

3 5 7 if 3

xf x

x x

⎧ <⎪⎪=⎨⎪ − − ≥⎪⎩

d) ( )5 if 3

3 5 7 if 3

xf x

x x

⎧ <⎪⎪=⎨⎪ + − ≥⎪⎩

20)

21) Find the difference quotient for ( ) 2 32 .f x x x= −

a) 2 23 4 3 2x x hx h h+ − + + b) 2 23 4 3 2x x hx h h− + − − +

c) 2 23 4 3 2x x hx h h− + + − + d) 2 23 4 3 2x x hx h h+ + + +

21)

For Exercises 22–23, use ( ) 3 11.

2 8

xf x

x

+=

−

22) Find ( )1f x− .

a) ( )1 8 11

2 3

xf x

x− − −

=−

b) ( )1 2 11

3 8

xf x

x− +

=−

c) ( )1 2 8

3 11

xf x

x− −

=+

d) ( )1 8 11

2 3

xf x

x− +

=−

22)

23) Find the range of ( ).f x

a) 3 3

, ,2 2

⎛ ⎞ ⎛ ⎞⎟ ⎟⎜ ⎜−∞ ∪ ∞⎟ ⎟⎜ ⎜⎟ ⎟⎜ ⎜⎝ ⎠ ⎝ ⎠ b) ( ) ( ), 4 4,−∞ ∪ ∞

c) 11 11

, ,3 3

⎛ ⎞ ⎛ ⎞⎟ ⎟⎜ ⎜−∞ − ∪ ∞⎟ ⎟⎜ ⎜⎟ ⎟⎜ ⎜⎝ ⎠ ⎝ ⎠ d)

2 2, ,3 3

⎛ ⎞ ⎛ ⎞⎟ ⎟⎜ ⎜−∞ ∪ ∞⎟ ⎟⎜ ⎜⎟ ⎟⎜ ⎜⎝ ⎠ ⎝ ⎠

23)

47



A flight instructor purchases a small airplane and depreciates its value linearly. The airplane is worth $45,000 after 10 years and $36,000 after 15 years. With this information, answer Exercises 24–26.

24) Find a linear equation giving the value, ,V of the airplane t years after purchase.

a) 1800 18000V t= + b) 1

350001800

V t=− +

c) 1800 45000V t=− + d) 1800 63000V t=− +

24)

25) What was the original value of the airplane?

a) $18,000 b) $70,000 c) $63,000 d) $45,000

25)

26) When will the airplane have no value?

a) 40 years b) 25 years c) 20 years d) 35 years

26)

48


Chapter 2 Test Form F Name Ratti & McWaters, College Algebra and Trigonometry and Precalculus: A Right Triangle Approach, 2e

For Exercises 1–2, use the points ( )9, 12− and ( )3,5 .−

1) Find the distance between the points.

a) 433 b) 145 c) 505 d) 85

1)

2) Find the midpoint between the points.

a) 7

3,2

⎛ ⎞⎟⎜ − ⎟⎜ ⎟⎜⎝ ⎠ b)

73,

2

⎛ ⎞⎟⎜− ⎟⎜ ⎟⎜⎝ ⎠ c)

176,

2

⎛ ⎞⎟⎜ − ⎟⎜ ⎟⎜⎝ ⎠ d)

176,

2

⎛ ⎞⎟⎜− ⎟⎜ ⎟⎜⎝ ⎠

2)

3) Write the equation, in standard form, for the

circle graphed to the right.

a) ( ) ( )2 22 4 25x y+ + + =

b) ( ) ( )2 22 4 25x y− + − =

c) ( ) ( )2 22 4 5x y+ + + =

d) ( ) ( )2 22 4 5x y− + − =

3)

4) Find the equation of the line passing through ( )21,11− that is perpendicular to the line

15 35 19.x y+ =

a) 3

27

y x=− + b) 3

207

y x= + c) 7

383

y x=− − d) 7

603

y x= +

4)


4 16.

4 12

xf x

x x

− −=

− −

a) [ ) ( ) ( )4, 2 2,6 6,− − ∪ − ∪ ∞ b) [ )4,− ∞

c) ( ) ( ], 2 2, 4−∞ − ∪ − − d) ( ], 4−∞ −

5)

6) State the x - and y -intercepts of 3 2 6 27.y x x= + −

a) ( )( ) ( )9,0 3,0 , 0,3− b) ( )( ) ( )0,9 0, 3 , 3,0−

c) ( )( ) ( )9,0 3,0 , 0, 3− − d) ( )( ) ( )0, 9 0,3 , 3,0− −

6)

49



For Exercises 7–9, use ( ) 2 3

5 if 6

3 if 6 8.

3 5if 8

7 2

x

x x x x

xx

x

⎧⎪⎪⎪− <−⎪⎪⎪⎪= − + − ≤ <⎨⎪⎪⎪ −⎪ ≥⎪⎪ −⎪⎩

7) Find ( )9 .f −

a) 2169− b) 5− c) 32

25− d)

131

7−

7)

8) Find ( )6 .f −

a) 23

19− b) 612− c) 684− d) 5−

8)

9) Find ( )8 .f

a) 19

9− b) 1472 c)

51

7 d) 5−

9)


10) State the domain of the function.

a) ( ] ( ], 2 4,10−∞ ∪

b) ( ] [ ), 4 1,7−∞ − ∪ −

c) ( ) [ ), 2 4,10−∞ ∪

d) ( ) ( ], 4 1,7−∞ − ∪ −

11) State the range of the function. a) ( ),−∞ ∞

b) ( ] [ ), 4 1,7−∞ − ∪

c) ( ] [ ), 4 1,7−∞ − ∪ −

d) ( ] ( ], 2 4,10−∞ ∪

10) 11)

12) Find the equation of the circle, in standard form, for 2 210 6 2 0.x x y y+ + − − =

a) ( ) ( )2 25 3 6x y+ + − = b) ( ) ( )2 2

5 3 36x y− + + =

c) ( ) ( )2 210 6 2x y+ + − = d) ( ) ( )2 2

5 3 36x y+ + − =

12)

50




13) When is the function increasing or decreasing?

a) Decreasing: ( ) ( ), 4 3, ;−∞ − ∪ ∞


b) Decreasing: ( )4,3 ;−

Increasing: ( ) ( ), 4 3,−∞ − ∪ ∞

c) Decreasing: ( )7,6 ;−

Increasing: ( ) ( ), 4 3,−∞ − ∪ ∞

d) Decreasing: ( ) ( ), 7 6, ;−∞ − ∪ ∞



minimum of the function? a) ( )8,8− b) ( )4,6−

c) ( )3, 7− d) ( )7,10


maximum of the function? a) ( )8,8− b) ( )4,6−

c) ( )3, 7− d) ( )7,10

13) 14) 15)

16) Test 2 2

34

3

8

x yy

x

−=

− for symmetry with respect to the x axis, the y axis, and the origin.

a) x axis b) y axis c) origin d) no symmetry

16)

For Exercises 17–18 use ( )2

2

6

3 9

xf x

x

−=

− + and ( ) 21 3 .g x x= −

17) Find ( )( ).f g x

a) ( )( )2

2

22 69

3

xf g x

x

−=

− b) ( )( ) 5

3 24

xf g x

x

+=

+

c) ( )( ) 5

3 18

xf g x

x

− +=

− d) ( )( ) 5

3 24

xf g x

x

−=

−

17)

18) What is the domain of ( )( )?f g x

a) ( ],7∞ b) ( ) ( ],6 6,7−∞ ∪

c) [ )7,− ∞ d) [ ) ( )7,6 6,− ∪ ∞

18)

51



19) Given the graph of ( ),f x draw the graph of ( )12 .

3f x−

a) b)

c)

d)

19)

52

Documents

Full file at ://fratstock.eu/sample/Test-Bank-College-Algebra-Trigonometry... · Full file at Chapter 2 Test Form A Name Ratti & McWaters, College Algebra and Trigonometry and Precalculus: