Free ACT Math: Functions Questions and Answers 3 Flashcards

The graph of f(x) is shifted 3 units to the right and 2 units down. If f(x) = x², what is the equation of the new function?

Answer: g(x) = (x − 3)² − 2

Horizontal shift right by 3: replace x with (x − 3). Vertical shift down by 2: subtract 2. Result: g(x) = (x − 3)² − 2.

For which value of x is the function f(x) = (x + 1)/(x² − x − 6) undefined?

Answer: x = 3 and x = −2

f(x) is undefined when the denominator equals zero. x² − x − 6 = (x − 3)(x + 2) = 0 → x = 3 or x = −2. Note: x = −1 makes the numerator zero but not the denominator, so it is defined (value = 0).

A function f has the property f(−x) = −f(x) for all x. What type of function is f?

Answer: An odd function

A function is odd if f(−x) = −f(x) for all x. Odd functions have 180° rotational symmetry about the origin. Even functions satisfy f(−x) = f(x).

If p(x) = 2x³ − x + 4, what is p(−1)?

Answer: 3

p(−1) = 2(−1)³ − (−1) + 4 = 2(−1) + 1 + 4 = −2 + 1 + 4 = 3.

If f(x) = 5x + 2 and g(x) = x − 4, what is (f − g)(x)?

Answer: 4x + 6

(f − g)(x) = f(x) − g(x) = (5x + 2) − (x − 4) = 5x + 2 − x + 4 = 4x + 6.

A function f is linear with f(2) = 7 and f(5) = 16. What is f(0)?

Answer: 1

Slope = (16 − 7)/(5 − 2) = 9/3 = 3. Using point-slope: f(x) = 3x + b. f(2) = 7: 6 + b = 7 → b = 1. So f(x) = 3x + 1. f(0) = 1.