Bluebook SAT Math: Advanced Functions Questions and Answers Flashcards

If f(x) = |2x - 6|, for how many values of x does f(x) = 4?

Answer: 2

|2x-6|=4 gives 2x-6=4 (x=5) or 2x-6=-4 (x=1), so there are exactly 2 solutions.

The function p(x) = x⁴ - 5x² + 4. How many real zeros does p(x) have?

Answer: 4

Let u=x²: u²-5u+4=(u-1)(u-4)=0 gives x=±1 or x=±2, yielding 4 real zeros.

If f(x) = (x+1)/(x-1), what is f(f(x))?

Answer: x

Replacing x with (x+1)/(x-1) and simplifying the compound fraction yields f(f(x)) = x.

For f(x) = 2^x, which transformation produces g(x) = 2^(x+3) - 4?

Answer: Shift left 3, down 4

Adding 3 inside the exponent shifts the graph left 3 units; subtracting 4 outside shifts it down 4 units.

If f is an odd function and f(3) = -5, what is f(-3)?

Answer: 5

For an odd function f(-x) = -f(x), so f(-3) = -f(3) = -(-5) = 5.

The function f(x) = a(x - 2)² - 3 passes through the point (0, 1). What is the value of a?

Answer: 1

Substitute (0, 1): 1 = a(0-2)² - 3 = 4a - 3, so 4a = 4 and a = 1.