Bluebook SAT Test Bluebook SAT Math: Advanced Functions 1

Question 1

If f(x) = x² + 6x + 5, which of the following is equivalent to f(x)?

Accepted Answer

(x + 1)(x + 5)

Answer

Factoring x² + 6x + 5 requires two numbers that multiply to 5 and add to 6. Those numbers are 1 and 5, giving (x + 1)(x + 5).

Question 2

If f(x) = 2x - 3 and g(x) = x + 4, what is g(f(x))?

Accepted Answer

2x + 1

Answer

g(f(x)) = g(2x - 3) = (2x - 3) + 4 = 2x + 1. Substitute f(x) into g(x) and simplify.

Question 3

The function p(x) = -x² + 4x - 1. What is the maximum value of p(x)?

Accepted Answer

3

Answer

The vertex x-coordinate is -b/(2a) = -4/(2·(-1)) = 2. Then p(2) = -(4) + 8 - 1 = 3. Since the parabola opens downward, this is the maximum.

Question 4

If f(x) = x² - 9, for which values of x does f(x) = 0?

Accepted Answer

x = 3 and x = -3

Answer

Setting x² - 9 = 0 gives x² = 9, so x = ±3. Both values satisfy the equation.

Question 5

A function is defined as h(x) = 3^(x-1). What is h(3)?

Accepted Answer

9

Answer

h(3) = 3^(3-1) = 3² = 9.

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