AP Calculus AB Questions and Free Response Questions

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Which of the following relations are functions?

I.y = -x + 2 II.x = -y + 2 III.x -y = 2 (2 points)

·	· All of them
·	· Choice I only
·	· Choice II only
·	· Choice III only

Find the range for f(x) = -x2 + 1, for x > 0.

a)	· y > 1
b)	· y ≥ 1
c)	· y < 1
d)	· y ≤ 1

Find the domain for f of x equals the quantity x minus 3 divided by quantity x minus 2 .

·	· x ≠ 2
·	· x ≠ −3
·	· x ≠ −3, −2
·	· x ≠ −2

Find the range of the function: f(x) = x + 5, for x ≠ 2.

·	· All real numbers
·	· y ≠ 2
·	· y ≠ 5
·	· y ≠ 7

Determine whether f(x) = 5x2 + 3x + 4 has a maximum or minimum.

·	· Maximum
·	· Minimum

Where is the function 4(x + 4)(x - 6)3 > 0?

·	· For x > -4 or x < 6
·	· For x < -4 or x > 6
·	· For no x values
·	· For all x values

For which x value would the graph of y = x2 - 25 be below the x-axis?

·	· 7
·	· 6
·	· 5
·	· 4

Find f(g(-4)) if f of x equals 7 divided by the quantity x plus two. and g(x) = (x + 5)2.

·	·
·	·
·	·
·	·

Find f[g(x)] if f(x) = x4 + 1 and g(x) = x2.

·	· (x4 + 1)2
·	· x8 + 1
·	· (x2 + 1)4
·	· None of these

10.

Find g(x) if g(x) is the resulting function from moving f(x) = (x + 1) right 2 units and up 5 units.

·	· g(x) = (x + 6) + 2
·	· g(x) = (x - 1) + 2
·	· g(x) = (x + 3) + 5
·	· g(x) = (x - 1) + 5

11.

Rewrite f(x) = sin(x) if the function is stretched vertically by a factor of 5.

·	· sin(5x)
·	· 5sin(x)
·	·
·	·

12.

What is the domain of y equals three divided by the quantity x plus two squared all minus four ? (2 points)

·	· All real numbers
·	· All real numbers less than -2
·	· All real numbers greater than -4
·	· All real numbers greater than -2
·	· All real numbers except -2

13.

Find the range of f of x equals 4 times the square root of the quantity x plus 4 .

·	· y > 4
·	· y ≥ 0
·	· y > 0
·	· All real numbers

14.

Is the function of f(x) = |-4x| + x4 even, odd, or neither?

·	· Odd
·	· Even
·	· Neither

15.

Find the period and amplitude for f(x) = 2sin(3x).

·	· Amplitude = 2, Period =
·	· Amplitude = 3, Period = π
·	· Amplitude = , Period = 2π
·	· Amplitude = 2, Period =

16.

Which one of the following is a function?

·	· 4x - 2y2 = 9
·	· 4x2 - 2y2 = 9
·	· 4x - 2y = 9

17.

Determine the range of f(x) = (x - 2)2 + 2.

·	· All real numbers
·	· y ≥ 0
·	· y > 2
·	· y ≥ 2

18.

Find the domain of f(x) = the square root of the quantity x plus 3

	· x > 3
	· x > -3
	· x ≥ -3
	· All real numbers

19.

Find the domain for the function f(x) = the quotient of the square root of the quantity x plus 5 and the quantity x minus 1

	· x ≠ 1
	· x ≥ -5
	· x ≥-5, x ≠ 1
	· All real numbers

20.

Which of the following statements are true about functions and relations?

	· All functions are relations.
	· All relations are functions.
	· A function may or may not be a relation.
	· The vertical line test will not work for piece-wise defined relations.

21.

A box is to be constructed from a sheet of cardboard that is 20 cm by 50 cm by cutting out squares of length x by x from each corner and bending up the sides.

What is the maximum volume this box could have? (Round your answer to two decimal places. Do not include units, for example, 10.22 cm would be 10.22.)

_______________

22.

To three decimal places, find the value of the first positive x-intercept for the function f(x) = 2cos(x + 4).

	· 1.712
	· 0.712
	· -2.429
	· -2.712

23.

Find the minimum value of the function f(x) = x2 + 9x - 16.

	· -36.250
	· -2.500
	· There is no minimum
	· Cannot be determined

24.

f(x) = 7x + 7, g(x) = 6x2

Find (fg)(x).

·	· 42x2 + 42x
·	· 6x2 + 7x + 7
·	· 42x + 42
·	· 42x3 + 42x2

25.

f as a function of x is equal to the square root of quantity 6 x plus 9 , g as a function of x is equal to the square root of quantity 6 x minus 9

Find (f + g)(x).

·	·
·	·
·	·
·	· 6x

26.

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

y = (x - 4)2 - 8

·	· Shift the graph of y = x2 right 4 units and then up 8 units.
·	· Shift the graph of y = x2 right 4 units and then down 8 units.
·	· Shift the graph of y = x2 left 4 units and then down 8 units.
·	· Shift the graph of y = x2 down 4 units and then left 8 units.
·

27.

Describe how to transform the graph of f into the graph of g.

f as a function of x is equal to the square root of x and g as a function of x is equal to the negative square root of x

·	· Reflect the graph of f across the y-axis.
·	· Reflect the graph of f across the y-axis and then reflect across the x-axis.
·	· Reflect the graph of f across the x-axis.
·	· The graph shifts left two units.

28.

Describe the transformations required to obtain the graph of the function f(x) from the graph of the function g(x).

f(x) = 6 cos x; g(x) = cos x

·	· Vertical stretch by a factor of 6
·	· Horizontal shrink by a factor of
·	· Horizontal stretch by a factor of 6
·	· Vertical shrink by a factor of

29.

Determine the domain of the function.

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

·	· x ≤ 9
·	· All real numbers except 9
·	· All real numbers
·	· x > 9

30.

Use the graph of f to estimate the local maximum and local minimum.

A piecewise function is shown with a curve intersecting the x axis at negative pi over two and pi over two terminating at pi, negative 1 and then a second curve originating at pi, 0 and intersecting the x axis at two pi.

·	· Local maximum: (0, 1); local minimum: and
·	· Local maximum: (0, 0) and approx (0, 1); local minimum:
·	· Local maximum: (0, 0); local minimum:
·	· Local maximum: (0, 1); local minimum: approx. (0, 0) and

31.

Determine algebraically whether the function is even, odd, or neither even nor odd.

f as a function of x is equal to 2 divided by x squared.

· Neither

· Even

· Odd

32.

State the vertical asymptote of the rational function.

f(x) = quantity x minus three times quantity x plus four divided by quantity x squared minus one.

·	· x = -3, x = 4
·	· x = 3, x = -4
·	· None
·	· x = 1, x = -1