AP Pre-Calculus FRQ Practice

Practice FRQ 1 of 2

1. The following functions are defined for this question:
g(x) = -0.2x^3 + 1.5x^2 + x - 4
h(x) = g(f(x))

The function

f

is increasing and is defined for all real numbers. The table gives values for

f(x)

at selected values of

x

. The function

g

is given by

g(x) = -0.2x^3 + 1.5x^2 + x - 4

. The function

h

is defined by

h(x) = (g \circ f)(x) = g(f(x))

g(x) = -0.2x^3 + 1.5x^2 + x - 4
h(x) = g(f(x))

x	f(x)
1	4
2	7
3	14
4	25
5	40

i. Find the value of

h(2)

as a decimal approximation, or indicate that it is not defined. Show the work that leads to your answer.

ii. Find the value of

f^{-1}(25)

, or indicate that it is not defined.

i. Find all values of

x

, as decimal approximations, for which

g(x) = 0

, or indicate that there are no such values.

ii. Determine the end behavior of

g

x

increases without bound. Express your answer using the mathematical notation of a limit.

i. Based on the table, which of the following function types best models function

f

: linear, quadratic, exponential, or logarithmic?

ii. Give a reason for your answer in part C(i) based on the relationship between the change in the output values of

f

and the change in the input values of

f

. Refer to the values in the table in your reasoning.

Practice FRQ 1 of 2

1. The following functions are defined for this question:
g(x) = -0.2x^3 + 1.5x^2 + x - 4
h(x) = g(f(x))

The function

f

is increasing and is defined for all real numbers. The table gives values for

f(x)

at selected values of

x

. The function

g

is given by

g(x) = -0.2x^3 + 1.5x^2 + x - 4

. The function

h

is defined by

h(x) = (g \circ f)(x) = g(f(x))

g(x) = -0.2x^3 + 1.5x^2 + x - 4
h(x) = g(f(x))

x	f(x)
1	4
2	7
3	14
4	25
5	40

i. Find the value of

h(2)

as a decimal approximation, or indicate that it is not defined. Show the work that leads to your answer.

ii. Find the value of

f^{-1}(25)

, or indicate that it is not defined.

i. Find all values of

x

, as decimal approximations, for which

g(x) = 0

, or indicate that there are no such values.

ii. Determine the end behavior of

g

x

increases without bound. Express your answer using the mathematical notation of a limit.

i. Based on the table, which of the following function types best models function

f

: linear, quadratic, exponential, or logarithmic?

ii. Give a reason for your answer in part C(i) based on the relationship between the change in the output values of

f

and the change in the input values of

f

. Refer to the values in the table in your reasoning.