College Math Placement Test Functions 5

Question 1

What is the average rate of change of f(x) = x² + 2x from x = 1 to x = 4?

Accepted Answer

7

Answer

Average rate of change = [f(4) - f(1)] / (4-1) = [(16+8) - (1+2)] / 3 = 21/3 = 7.

Question 2

If f(x) = log₂(x), then f(32) equals:

Accepted Answer

5

Answer

log₂(32) = log₂(2⁵) = 5.

Question 3

The function f(x) = -2(x - 1)² + 8 has a maximum value of:

Accepted Answer

8

Answer

Since a = -2 < 0 the parabola opens downward, and the vertex at (1, 8) gives the maximum value of 8.

Question 4

Which of the following pairs of functions are inverses of each other?

Accepted Answer

f(x) = x + 5 and g(x) = x - 5

Answer

f(g(x)) = (x-5)+5 = x and g(f(x)) = (x+5)-5 = x, confirming they are inverses.

Question 5

If f(x) = x/(x-2), what happens to f(x) as x approaches 2?

Accepted Answer

f(x) approaches infinity

Answer

As x → 2, the denominator approaches 0 while the numerator approaches 2, so f(x) → ±∞.

College Math Placement Test Practice Test