Bluebook SAT Test Bluebook SAT Math: Advanced Functions Questions and Answers 2

Question 1

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

Accepted Answer

3

Answer

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

Question 2

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

Accepted Answer

256

Answer

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.

Question 3

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

Accepted Answer

3

Answer

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

Question 4

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

Accepted Answer

3x² + 1

Answer

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

Question 5

Which of the following is an even function?

Accepted Answer

f(x) = x⁴ - 2x²

Answer

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

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