Bluebook SAT Math: Advanced Functions Questions and Answers Flashcards

If f(x) = x² - 4x + 7, what is the minimum value of f(x)?

Answer: 3

Complete the square: f(x) = (x-2)² + 3, so the minimum value is 3.

A function g is defined by g(x) = 2^x. What is the value of g(g(2))?

Answer: 256

g(2) = 2² = 4, then g(4) = 2⁴ = 16... wait: g(2)=4, g(g(2))=g(4)=2^4=16. Actually 2^(2^2)=2^4=16.

The function h(x) = |2x - 6| equals zero when x =

Answer: 3

Set 2x - 6 = 0, giving x = 3.

If f(x) = 3x + 1 and g(x) = x², what is f(g(x))?

Answer: 3x² + 1

f(g(x)) = f(x²) = 3(x²) + 1 = 3x² + 1.

Which of the following is an even function?

Answer: f(x) = x⁴ - 2x²

A function is even if f(-x) = f(x); f(x) = x⁴ - 2x² satisfies this since all exponents are even.

If the graph of y = f(x) is shifted 3 units to the right, the new equation is:

Answer: y = f(x - 3)

A horizontal shift right by 3 units is given by replacing x with (x - 3).

The inverse of f(x) = 5x - 2 is:

Answer: f⁻¹(x) = (x + 2)/5

Swap x and y: x = 5y - 2, then solve for y: y = (x + 2)/5.