Edison CollegeMAC 1105 Summer 2008 Practice Exam #2Dr. Schnackenberg

If you do not agree with the given answers, choose "E" for "None of the above".MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Find the slope of the line passing through the pair of points or state that the slope is undefined.1) 1)(-5, -4) and (-2, -4)

A) -83 B) 0 C) 8

7 D) Undefined

Use the given conditions to write an equation for the line in point-slope form.2) 2)Passing through (8, 2) and (4, 5)

A) y + 2 = -34

(x + 8) or y + 5 = -34

(x + 4) B) y - 2 = -34

(x - 8) or y - 5 = -34

(x - 4)

C) y - 2 = 8(x + 8) or y - 5 = 4(x - 2) D) y - 2 = -34

(x - 4) or y - 5 = -34

(x - 8)

Use the given conditions to write an equation for the line in slope-intercept form.3) 3)Passing through (7, 2) and (2, 8)

A) y = mx +525 B) y =

65

x +525

C) y - 2 = -65

(x - 7) D) y = -65

x +525

Graph the equation in the rectangular coordinate system.4) 4)x = 3

1

A) B)

C) D)

Determine the slope and the y-intercept of the graph of the equation.5) 5)7x + y - 5 = 0

A) m = -17

; 0, 57 B) m =

75

; 0, 15 C) m = -7; (0, 5) D) m = 7; (0, 5)

Use the given conditions to write an equation for the line in the indicated form.6) 6)Passing through (5, 4) and perpendicular to the line whose equation is y = 3x + 7;

point-slope form

A) y - 4 = -13

(x - 5) B) y = - 3x - 17

C) y - 5 =13

(x - 4) D) y - 4 =13

(x + 5)

7) Passing through (5, 3) and parallel to the line whose equation is y = -15

x + 5;

slope-intercept form

7)

A) y = -15

x - 4 B) y = -15

x + 4 C) y =15

x - 4 D) y = - 5x - 20

2

Solve the problem.8) 8)A school has just purchased new computer equipment for $18,000.00. The graph shows the

depreciation of the equipment over 5 years. The point (0, 18,000) represents the purchase price andthe point (5, 0) represents when the equipment will be replaced. Write a linear equation inslope-intercept form that models the value of the equipment, y, x years after purchase. Use themodel to predict the value of the equipment after 3 years?

A) y = - 3600x + 18,000;value after 3 years is $7200.00;

B) y = - 18,000x + 18,000;value after 3 years is $-36,000.00

C) y = 3600x - 18,000;value after 3 years is $7200.00

D) y = 18,000x + 5;value after 3 years is $7200.00

Find the domain and range of the relation.9) 9){(4, -1), (-5, 7), (8, -7), (-2, -4), (2, 1)}

A) domain = {-7, 4, -1, 2, 1}; range = {-2, -4, -5, 7, 8}B) domain = {-2, -5, 8, 4, 2}; range = {-4, 7, -7, -1, 1}C) domain = {-2, -4, -5, 7, 8}; range = {-7, 4, -1, 2, 1}D) domain = {-4, 7, -7, -1, 1}; range = {-2, -5, 8, 4, 2}

Determine whether the relation is a function.10) 10){(-6, 9), (-6, 5), (1, 9), (5, 3), (8, 1)}

A) Function B) Not a function

Determine whether the equation defines y as a function of x.11) 11)y = 7x - 1

A) y is a function of x B) y is not a function of x

Evaluate the function at the given value of the independent variable and simplify.12) 12)f(x) = 3x2 - 4x + 6; f(x - 1)

A) -10x2 + 3x + 13 B) 3x2 - 10x + 13 C) 3x2 + 14x + 5 D) 3x2 - 10x + 5

13) f(x) =x2 + 5x3 + 6x

; f(-2) 13)

A) -920 B) -

15 C) -

98 D) -

92

3

Find and simplify the difference quotient f(x + h) - f(x)h

, h 0 for the given function.

14) 14)f(x) = x2 + 8x - 1

A) 2x + h - 1 B) 1

C) 2x2 + 2x + 2xh + h2 + h - 2h

D) 2x + h + 8

15) 15)f(x) = x2 + 4x - 4

A) 2x + h + 4 B) 2x + h - 4

C) 2x2 + 2x + 2xh + h2 + h - 8h

D) 1

Evaluate the piecewise function at the given value of the independent variable.16) 16)

f(x) =

x - 3 if x > -5

-(x - 3) if x -5

Determine f(-8).A) -11 B) -19 C) -8 D) 11

Find the domain of the function.

17) f(x) =2x

x - 7 17)

A) (- , 0) or (0, ) B) (- , 7) C) (- , 7) or (7, ) D) (- , )

18) f(x) =x + 7

(x + 5)(x + 2)18)

A) (- , -7) or (-7, -5) or (-5, -2) or (-2, ) B) [-7, -5) or (-5, -2) or (-2, )C) (- , ) D) (0, )

4

Use the graph to determine the function's domain and range.19) 19)

A) domain: (- , )range: (- , )

B) domain: (- , )range: (- , 5]

C) domain: (- , -2]range: (- , 5]

D) domain: (- , -2) or (-2, )range: (- , 5) or (5, )

Use the vertical line test to determine whether y is a function of x.20) 20)

A) Yes B) No

5

Identify the intervals where the function is changing as requested.21) 21)Increasing

A) (-3, 3) B) (-2, ) C) (-3, ) D) (-2, 2)

Use the graph of the given function to find any relative maxima and relative minima.22) 22)f(x) = x3 - 3x2 + 1

A) maximum: none; minimum: (2, -3) B) no maximum or minimumC) maximum: (0, 1); minimum: none D) maximum: (0, 1); minimum: (2, -3)

Determine whether the given function is even, odd, or neither.23) 23)f(x) = 2x2 + x4

A) Odd B) Neither C) Even

6

Use possible symmetry to determine whether the graph is the graph of an even function, an odd function, or a functionthat is neither even nor odd.

24) 24)

A) Odd B) Even C) Neither

If f(x) = int (x), find the function value.25) 25)f(85.10)

A) 84.1 B) 86 C) 85 D) 85.10

Use the shape of the graph to name the function.26) 26)

A) Constant function B) Standard quadratic functionC) Standard cubic function D) Square root function

7

Begin by graphing the standard quadratic function f(x) = x2 . Then use transformations of this graph to graph the givenfunction.

27) 27)g(x) = x2 + 2.

A) B)

C) D)

8

Begin by graphing the standard square root function f(x) = x . Then use transformations of this graph to graph the givenfunction.

28) 28)h(x) = x + 1

A) B)

C) D)

9

29) 29)g(x) = - x + 3

A) B)

C) D)

10

Begin by graphing the standard quadratic function f(x) = x2 . Then use transformations of this graph to graph the givenfunction.

30) h(x) =12

(x - 2)2 30)

A) B)

C) D)

11

Begin by graphing the standard absolute value function f(x) = x . Then use transformations of this graph to graph thegiven function.

31) g(x) =13

x - 2 - 2 31)

A) B)

C) D)

Given functions f and g, perform the indicated operations.32) 32)f(x) = 4x - 6, g(x) = 7x - 9

Find f - g.A) -3x + 3 B) 3x - 3 C) 11x - 15 D) -3x - 15

For the given functions f and g , find the indicated composition.33) 33)f(x) = 18x2 - 5x, g(x) = 13x - 10

(f g)(1)A) 39 B) 12 C) 159 D) 147

12

34) 34)f(x) = -4x + 8, g(x) = 2x + 9(g f)(x)

A) -8x - 7 B) -8x + 25 C) 8x + 25 D) -8x + 44

Find the domain of the composite function f g.

35) f(x) = x + 5, g(x) =10

x + 7 35)

A) (- , -7) or (-7, -5) or (-5, ) B) (- , -7) or (-7, )C) (- , -12) or (-12, ) D) (- , )

Express the given function h as a composition of two functions f and g so that h(x) = (f g)(x).36) 36)h(x) = 8x + 8

A) f(x) = -x ; g(x) = 8x - 8 B) f(x) = x; g(x) = 8x + 8C) f(x) = x ; g(x) = 8x + 8 D) f(x) = - x ; g(x) = 8x + 8

Determine which two functions are inverses of each other.

37) f(x) =x + 5

4g(x) = 4x + 5 h(x) =

x - 54 37)

A) g(x) and h(x) B) f(x) and h(x) C) None D) f(x) and g(x)

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

38) f(x) =5x - 3

8 38)

A) f-1(x) =8

5x - 3 B) f-1(x) =8

5x + 3 C) f-1(x) =8x - 3

5 D) f-1(x) =8x + 3

5

Does the graph represent a function that has an inverse function?39) 39)

A) Yes B) No

13

Use the graph of f to draw the graph of its inverse function.40) 40)

A) B)

14