PRE CALCULUS Functions 5

Question 1

What is the domain of f(x) = 1 / (x² - 9)?

Accepted Answer

All real numbers except x = ±3

Answer

The denominator x² - 9 = 0 when x = ±3, so those values are excluded from the domain.

Question 2

If f(x) = 5 - 2x, which equation represents f(f(x))?

Accepted Answer

4x - 5

Answer

f(f(x)) = f(5 - 2x) = 5 - 2(5 - 2x) = 5 - 10 + 4x = 4x - 5.

Question 3

The graph of y = f(x) + 3 is the graph of y = f(x) shifted:

Accepted Answer

Up 3 units

Answer

Adding a constant outside the function shifts the graph vertically upward by that amount.

Question 4

What is the range of f(x) = -x² + 5?

Accepted Answer

y ≤ 5

Answer

Since -x² ≤ 0 for all x, -x² + 5 ≤ 5, so the range is (-∞, 5].

Question 5

For the piecewise function f(x) = { x + 2 if x < 0; x² if x ≥ 0 }, what is f(-3) + f(2)?

Accepted Answer

3

Answer

f(-3) = -3 + 2 = -1 (since -3 < 0) and f(2) = 2² = 4 (since 2 ≥ 0), so -1 + 4 = 3.

PRE CALCULUS Practice Test