Identify the vertical asymptotes of f(x) = 2 over quantity x squared plus 3 x minus 10.

Choose only one answer for Multiple Choice.

1.

Determine the domain of the function.

f as a function of x is equal to the square root of one minus x.

·

· All real numbers

·

· x > 1

·

· x ≤ 1

·

· All real numbers except 1

2.

Determine the domain of the function.

f as a function of x is equal to the square root of x plus three divided by x plus eight times x minus two.

· All real numbers except -8, -3, and 2

· x ≥ 0

· All real numbers

· x ≥ -3, x ≠ 2

3.

f(x) = 3x + 2; g(x) = 3x - 5

Find f/g.

· (f/g)(x) = Quantity three x minus five divided by three x plus two. ; domain {x|x ≠ - Two over three.}

· (f/g)(x) = Quantity three x plus two divided by three x minus five. ; domain {x|x ≠ Five over three.}

· (f/g)(x) = Quantity three x minus five divided by three x plus two; domain {x|x ≠ Five over three.}

· (f/g)(x) = Quantity three x plus two divided by three x minus five ; domain {x|x ≠ - Two over three.}

4.

Use your graphing calculator to graph f(x) = |x + 1| and determine where the function is increasing and decreasing.

· Increasing x > -1; Decreasing x < -1

· Increasing x < 1; Decreasing x > 1

· Increasing x < -1, Decreasing x > -1

· Increasing x > 1; Decreasing x < 1

5.

Select true or false:

The function -3(x + 2)(x - 5)3 > 0, when x < -2 or x > 5.

·

· True

·

· False

6.

f(x) = 2x + 6, g(x) = 4x2

Find (f + g)(x).

· 8x3 + 24x

· Quantity two x plus 6 divided by four x squared.

· 4x2 + 2x + 6

· -4x2 + 2x + 6

7.

f(x) = Square root of quantity x plus eight.; g(x) = 8x - 12

Find f(g(x)).

· f(g(x)) = 2Square root of quantity two x plus one.

· f(g(x)) = 8Square root of quantity x plus eight. - 12

· f(g(x)) = 2Square root of quantity two x minus one.

· f(g(x)) = 8Square root of quantity two x plus one.

8.

Describe how the graph of y = x2 can be transformed to the graph of the given equation:

y = x2 - 20

·

· Shift the graph of y = x2 left 20 units.

·

· Shift the graph of y = x2 up 20 units.

·

· Shift the graph of y = x2 down 20 units.

·

· Shift the graph of y = x2 right 20 units.

9.

Is the function of f(x) = |4x| + 3 over x even, odd, or neither?

· Even

· Odd

· Neither

10.

State the domain of the rational function.

f(x) = thirteen divided by quantity ten minus x.

· All real numbers except -10 and 10

· All real numbers except 13

· All real numbers except 10

· All real numbers except -13 and 13

11.

If limit as x approaches a of f of x equals four and limit as x approaches a of g of x equals two, then limit as x approaches a of the quantity three times f of x squared minus four times g of x equals forty.

· True

· False

12.

Find the limit of the function algebraically.

limit as x approaches zero of quantity negative seven plus x divided by x squared.

·

· Does not exist

·

· 7

·

· 0

·

· -7

13.

Find limit as x approaches 3 for f of x equals the quantity 3x plus 1 for x less than or equal to 32 and f of x equals 2 times x squared for x greater than 3.

· 10

· 18

· Does not exist

· 10 or 18

14.

Evaluate limit as x goes to 0 of 1 minus the quotient of the square of cosine of x, and x.

·

·

· 0

·

· −∞

·

· ∞

·

· Does not exist

15.

Evaluate limit as x goes to 0 of the quotient of the quantity x raised to the 4th power minus 1 and x minus 1.

·

·

· 1

·

· 0

·

· zero over zero

·

· Does not exist

16.

Evaluate limit as x goes to infinity of the quotient of 4 times x cubed plus 2 times x squared plus 3 times x and negative 9 times x squared plus 5 times x plus 5

·

· ∞

·

· -∞

·

· 0

·

· 4 over 9

17.

Find the equation of the horizontal asymptote for the function, f of x equals the quotient of the quantity x minus 100 and x raised to the 2nd power minus 100 .

· There is no horizontal asymptote.

· y = 0

· y = 1

· y = x

18.

Which of the following is false for f of x equals the quotient of 5 times x cubed minus 5 times x squared minus 10 times x and the quantity 2 times x raised to the fifth power minus 2 times x ?

· The x-axis is an asymptote of f(x).

· x = -1 is not an asymptote of f(x).

· x = 1 is an asymptote of f(x).

· The y-axis is an asymptote of f(x).

19.

To two decimal places, find the value of k that will make the function f(x) continuous everywhere.

f of x equals the quantity 3 times x plus k for x less than or equal to negative 4 and is equal to k times x squared minus 5 for x greater than negative 4

· 11.00

· -2.47

· -0.47

· None of these

20.

Where is f of x equals the quotient of x minus 1 and the quantity x squared minus 5 times x plus 4 discontinuous?

· f(x) is continuous everywhere

· 1

· 1, 4

· 4

21.

Is the function f of x equals the quantity 2 times x plus 1 for x less than or equal to 4 and is equal to x squared plus 12 for x greater than 4 continuous?

· Yes

· No

22.

List the discontinuities for the function f(x) = cot( 5x over 3 ).

· There are no discontinuities.

· n( pi over 2 ), where n is an integer

· n( pi over 3 ), where n is an integer

· n( three pi over five ), where n is an integer

23.

Which of the following is true for f of x equals the quotient of the quantity x squared minus 9 and the quantity x minus 3 ?

· There is a removable discontinuity at x = 3.

· There is a non-removable discontinuity at x = 3.

· The function is continuous for all real numbers.

24.

What is the instantaneous slope of y = negative 5 over x at x = 5?

·

· 1 over 5

·

· 1

·

· -1

·

· negative 1 over 5

25.

What is the average rate of change of y with respect to x over the interval [-2, 6] for the function y = 5x + 2?

·

· 5

·

· 2

·

· 1 over 5

·

· 10

26.

What is the slope for the function y = -3x2 + 2 at the point x = 2?

· -4

· -10

· -12

· The slope cannot be determined.

27.

The surface area, S, of a sphere of radius r feet is S = S(r) = 4πr2. Find the instantaneous rate of change of the surface area with respect to the radius r at r = 4.

·

· 32π

·

· 16π

·

· 64π

·

· 4π

28.

A ball is thrown vertically upward from the top of a 100 foot tower, with an initial velocity of 10 ft/sec. Its position function is s(t) = -16t2 + 10t + 100. What is its velocity in ft/sec when t = 2 seconds?

·

· -32

·

· -38

·

· -54

·

· 80

29.

Using the graph of f(x) below, find limit as x approaches 3 of f of x.

A graph is shown beginning at the open point negative two comma negative four continuing to the open point negative one negative one up to a maximum at zero comma zero and back down to the open point one comma negative one. The graph begins again at the closed point one comma two and then continues down to infinity along the asymptote x equals three then from negative infinity along the asymptote of x equals three the graph increases to the closed point five comma zero. A noncontinuous closed point exists at negative one comma negative two.

·

· −5

·

· −∞

·

· 0

·

· 1.7

30.

Find limit as x approaches zero of the quotient of sine of negative 2x and the sine of negative 5x..

· Does not exist

· 0

· two fifths.

· five halves.

31.

What is limits as x approaches negative 4 from the right of the quotient of x and the quantity x plus 4.?

·

· ∞

·

· 0

·

· −4

·

· −∞

32.

What is limit as x approaches 9 of the quotient of the quotient of the quantity 9 minus x and the square root of x minus 2.?

·

· −6

·

· 0

·

· 1

·

· Does not exist

33.

Find the limit of the function by using direct substitution.

limit as x approaches zero of quantity x squared minus five.

· Does not exist

· 0

· 5

· -5

34.

Use your graphing calculator to evaluate limit as x goes to infinity of the quantity 1 plus x raised to the power of 3 divided by x .

· 0

· π

· e3

· 1

35.

Use your calculator to select the best answer below:

limit as x goes to infinity of the quotient of the quantity the natural log of the absolute value of x minus 1 and the quantity cosine x raised to the x power

·

· does not exist

·

· 1

·

· -1

·

· 0

36.

limit as x approaches a of the quotient of the quantity x minus a and the quantity the square root of x minus the square root of a equals

·

· negative 2 times the square root of a

·

· 2 times the square root of a

·

· the square root of a

·

· 2a

37.

Find the limit as x goes to 0 of the quotient of the quantity x plus 1 minus the square of cosine x and 3 times the sine of x .

· does not exist

· 3

· 0

· one third

38.

If limit as x approaches zero of f of x equals two and limit as x approaches zero of g of x equals six , then find limit as x approaches zero of the quantity f of x plus g of x squared .

·

· 64

·

· -4

·

· 16

·

· 28

39.

Evaluate limit as x approaches 0 of the quotient of the absolute value of x and x .

·

· 0

·

· does not exist

·

· 1

·

· -1

40.

Evaluate limit as x goes to 3 of the quotient of the quantity 1 divided by x minus 1 third and the quantity x minus .

·

· negative 1 over 9

·

· 1 over 9

·

· 1 over 27

·

· 1 over 3

41.

Evaluate limit as x goes to 0 of the quotient of the sine of 5 times x and 6x .

·

· 1

·

· 5 over 6

·

· 1 over 6

·

· does not exist

42.

If f is a continuous function with even symmetry and limit as x approaches infinity of f of x equals 10 , which of the following statements must be true?

I.the limit as x goes to negative infinity of f of x equals 10 II.There are no vertical asymptotes. III.The lines y = 10 and y = -10 are horizontal asymptotes.

·

· I only

·

· II only

·

· I and II only

·

· All statements are true.

43.

What are the horizontal asymptotes of the function f of x equals the quotient of the square root of the quantity x squared plus 1 and x ?

·

· y = 1 only

·

· y = -1 only

·

· y = 0

·

· y = -1 and y = 1

44.

Which one or ones of the following statements is/are true?

I. If the line y = 2 is a horizontal asymptote of y = f(x), then f is not defined at y = 2.

II. If f(5) > 0 and f(6) < 0, then there exists a number c between 5 and 6 such that f(c) = 0.

III. If f is continuous at 2 and f(2)=8 and f(4)=3, then the limit as x approaches 2 of f of the quantity 4 times x squared minus 14 equals 8.

·

· All statements are true.

·

· I only

·

· II only

·

· III only

45.

Find limit as x goes to infinity of the quotient of 7 times x cubed minus 3 times x squared plus 3 times x and negative 8 times x squared plus 4 times x plus 3

·

· negative 7 over 8

·

· 0

·

· -∞

·

· ∞

46.

Evaluate limit as x goes to 2 from the left of the quotient of x and the quantity the square root of the quantity x squared minus 4 .

·

· 1

·

· 0

·

· 3

·

· does not exist

47.

Which of the following are the equations of all horizontal and vertical asymptotes for the graph of f of x equals x divided by the quantity x times the quantity x squared minus 16 ?

· y = 0, x = -4, x = 4

· y = 1, x = -4, x = 4

· y = 0, x = -4, x = 0, x = 4

· y = 1, x = -4, x = 0, x = 4

48.

Evaluate limit as x approaches 1 at f of x for f of x equals the quantity 5 times x minus 11 for x less than 1, equals 1 for x equals 1 and equals negative 3 times x plus 6 for x greater than 1 .

· 3

· -6

· 1

· does not exist

49.

Where is f of x equals the quotient of x plus 3 and x squared plus 2 times x minus 3 discontinuous?

· f is continuous everywhere

· x = 1

· x = -3

· x = -3 and x = 1

50.

Which of the following are continuous for all real values of x?

I. f of x equals the quotient of the quantity x squared plus 5 and the quantity x squared minus 1

II. g of x equals the quotient of 3 and the quantity x squared plus 1

III. h of x equals the absolute value of the quantity x minus 1

· II and III only

· I and II only

· I only

· II only

51.

Which of the following must be true for the graph of the function f of x equals the quotient of the quantity x squared minus 9 and the quantity 3 times x minus 9?

There is:

I. a vertical asymptote at x = 3

II. a removable discontinuity at x = 3

III. an infinite discontinuity at x = 3

· I only

· II only

· III only

· I, II, and III

52.

What is the average rate of change of y with respect to x over the interval [-3, 5] for the function y = 2x + 2?

·

· 16

·

· one half

·

· 2

·

· one fourth

53.

What is the instantaneous slope of y = negative two over x at x = 3?

·

· negative 2 over 9

·

· 2 over 9

·

· 2 over 3

·

· negative 2 over 3

54.

The height, s, of a ball thrown straight down with initial speed 32 ft/sec from a cliff 48 feet high is s(t) = -16t2 - 32t + 48, where t is the time elapsed that the ball is in the air. What is the instantaneous velocity of the ball when it hits the ground?

·

· 64 ft/sec

·

· 0 ft/sec

·

· 256 ft/sec

·

· -64 ft/sec

55.

The surface area of a right circular cylinder of height 5 feet and radius r feet is given by S(r)=2πrh+2πr2. Find the instantaneous rate of change of the surface area with respect to the radius, r, when r = 6.

·

· 24π

·

· 34π

·

· 64π

·

· 20π

56.

Use your graphing calculator to evaluate limit as x goes to infinity of the quantity x raised to the power of 1 divided by 2 times x .

·

· 1

·

· e divided by 2

·

· π

·

· 0

57.

Describe the discontinuity for the function f of x equals the quotient of the quantity x squared plus 9 and the quantity x minus 3 .

·

· There is a hole at x = -9.

·

· There is a vertical asymptote at x = 3.

·

· There is a removable discontinuity at x = 3.

·

· There is no discontinuity at x = 3.

58.

Find limit as x goes to 0 of the quotient of the sine of negative 4 times x and the sine of negative 2 times x .

· 1 over 2

· does not exist

· 2

· 0

59.

Evaluate limit as x goes to negative 8 from the right of the quotient of x and the quantity x plus 8 .

·

· ∞

·

· -∞

·

· 0

·

· -8

60.

Evaluate limit as x goes to infinity of the quotient of the negative 4 times x cubed plus 3 times x squared plus 6 times x and the quantity 6 times x squared minus 4 times x minus 5 .

· -2

· negative 2 over 3

· 0

· -∞

61.

Which of the following is the graph of which function has y = -1 as an asymptote?

· y equals negative x divided by the quantity 1 minus x

· y = ln(x + 1)

· y equals x divided by the x plus 1

· y equals x divided by the quantity 1 minus x

62.

If f of x equals the quotient of the quantity x squared minus 16 and the quantity x plus 4 is continuous at x = -4, find f(-4).

·

· 4

·

· -4

·

· 8

·

· -8

63.

Where is f of x equals the quotient of the quantity x plus 4 and x squared plus 6 times x plus 8 discontinuous?

· f(x) is continuous everywhere

· x = -4

· x = -2

· x = -4 and x = -2

64.

If f(x) is discontinuous, determine the reason.

f of x equals the quantity x squared plus 4 for x less than or equal to 1 and equals x plus 4 for x greater than 1

· f(x) is continuous for all real numbers

· The limit as x approaches 1 does not exist

· f(1) does not equal the limit as x approaches 1

· f(1) is not defined

65.

If f(x) is a continuous function defined for all real numbers, f(-1) = 1, f(-5) = -10, and f(x) = 0 for one and only one value of x, then which of the following could be that x value?

·

· -6

·

· -5

·

· -4

·

· 0

66. Use the graph below to list the x value(s) where the limits as x approaches from the left and right of those integer values(s) are not equal.

A graph is shown beginning at the open point negative two comma negative four continuing to the open point negative one negative one up to a maximum at zero comma zero and back down to the open point one comma negative one. The graph begins again at the closed point one comma two and then condinues down to infinity along the asymptote x equals three then from negative infinity along the asymptote of x equals three the graph increases to the closed point five comma zero. A noncontinuous closed point exists at negative one comma negative two.

_______________________________

67.

Find limit as x approaches 4 of the quotient of the quantity the square root of the quantity 3 times x plus 4 minus the square root of 4 times x and the quantity x squared minus 4 times x . You must show your work or explain your work in words.

_______________________________

68.

Find limit as x approaches 4 from the left of the quotient of the absolute value of the quantity x minus 4, and the quantity x minus 4 . You must show your work or explain your work in words.

_______________________________

69.

A ball's position, in meters, as it travels every second is represented by the position function s(t) = 4.9t2 + 350.

What is the velocity of the ball after 2 seconds?

Include units in your answer.

_______________________________

70.

The cost in dollars of producing x units of a particular telephone is C(x) = x2 - 2500. (10 points)

1. Find the average rate of change of C with respect to x when the production level is changed from x = 100 to x = 103. Include units in your answer.

2. Find the instantaneous rate of change of C with respect to x when x = 100. Include units in your answer.

_______________________________

71.

State the domain and range for the function f(x) = 2x2 - 7.

_____________________________

72. Show that the function f(x) = x3 + five over x is even, odd, or neither.

_____________________________

73. Determine the equation of a line, in slope-intercept form, that passes through the points (3, 6) and (6, 8).

____________________________

74. Write the equation of the function g(x) if g(x) = f(x - 2) +4 and f(x) = x3 + 2.

_____________________________

75. Identify the maximum and minimum values of the function y = 10 cos x in the interval [-2π, 2π]. Use your understanding of transformations, not your graphing calculator.

_____________________________

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