Bluebook SAT Math: Advanced Functions Questions and Answers Flashcards

If f(x) = x³ - x, which of the following is true?

Answer: f is an odd function

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

The range of f(x) = -x² + 6 is:

Answer: y ≤ 6

Since -x² ≤ 0 for all x, f(x) = -x² + 6 ≤ 6, with maximum 6 at x = 0.

If h(t) = -16t² + 64t represents the height (ft) of a ball after t seconds, at what time does it reach maximum height?

Answer: t = 2

The vertex is at t = -b/(2a) = -64/(2·(-16)) = 64/32 = 2 seconds.

If f(x) = 4x + k and f(3) = 20, what is k?

Answer: 8

4(3) + k = 20, so 12 + k = 20, giving k = 8.

The graph of y = f(x) is reflected across the x-axis. The new equation is:

Answer: y = -f(x)

Reflecting across the x-axis negates all y-values, replacing f(x) with -f(x).

For what value of x does f(x) = x² - 9 equal zero (positive root)?

Answer: 3

x² - 9 = 0 gives x² = 9, so x = ±3; the positive root is 3.

If f(x) = 1/(x - 3), what value of x is NOT in the domain?

Answer: 3

The denominator cannot be zero: x - 3 ≠ 0, so x = 3 is excluded from the domain.