PRE CALCULUS Pre-Calculus Functions 3

Question 1

Which of the following functions is odd?

Accepted Answer

f(x) = x³ - x

Answer

f(-x) = (-x)³ - (-x) = -x³ + x = -(x³ - x) = -f(x), confirming it is odd.

Question 2

The graph of y = f(2x) compared to y = f(x) is:

Accepted Answer

Compressed horizontally by a factor of 2

Answer

Replacing x with 2x compresses the graph horizontally by a factor of 2.

Question 3

If f(x) = 1/(x - 2), which value is NOT in the domain?

Accepted Answer

x = 2

Answer

The denominator equals zero when x = 2, making f undefined there.

Question 4

For f(x) = x² and g(x) = x + 3, what is (g ∘ f)(x)?

Accepted Answer

x² + 3

Answer

(g ∘ f)(x) = g(f(x)) = g(x²) = x² + 3.

Question 5

What does the vertical line test determine?

Accepted Answer

Whether a graph represents a function

Answer

If any vertical line crosses a graph more than once, the graph does not represent a function.

PRE CALCULUS Practice Test