Bluebook SAT Test Bluebook SAT Math: Advanced Functions Questions and Answers 4

Question 1

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

Accepted Answer

f is an odd function

Answer

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

Question 2

The range of f(x) = -x² + 6 is:

Accepted Answer

y ≤ 6

Answer

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

Question 3

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

Accepted Answer

t = 2

Answer

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

Question 4

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

Accepted Answer

8

Answer

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

Question 5

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

Accepted Answer

y = -f(x)

Answer

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

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