Bluebook SAT Test Bluebook SAT Math: Advanced Functions Questions and Answers 5

Question 1

The function f(x) = 2(x - 1)² + 3 has its vertex at:

Accepted Answer

(1, 3)

Answer

In vertex form f(x) = a(x - h)² + k, the vertex is (h, k) = (1, 3).

Question 2

If f(x) = x² and g(x) = x - 2, what is (f ∘ g)(5)?

Accepted Answer

9

Answer

(f ∘ g)(5) = f(g(5)) = f(3) = 3² = 9.

Question 3

Which function has a horizontal asymptote at y = 0?

Accepted Answer

f(x) = 3/x

Answer

As x → ±∞, 3/x → 0, so the horizontal asymptote is y = 0.

Question 4

If f(x) = 2ˣ, what is the value of f(-3)?

Accepted Answer

1/8

Answer

f(-3) = 2⁻³ = 1/2³ = 1/8.

Question 5

A function f is defined as f(x) = x² - 6x + 9. What is the simplified form?

Accepted Answer

(x - 3)²

Answer

x² - 6x + 9 is a perfect square trinomial equal to (x - 3)².

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