Bluebook SAT Test Bluebook SAT Math: Advanced Functions 1 — Questions and Answers
Question 1: If f(x) = x² + 6x + 5, which of the following is equivalent to f(x)?
- (x + 1)(x + 5) (Correct answer)
- (x + 2)(x + 3)
- (x - 1)(x - 5)
- (x + 6)(x + 1)
Correct answer: (x + 1)(x + 5)
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))?
- 2x + 1 (Correct answer)
- 2x - 7
- 2x + 7
- x + 1
Correct answer: 2x + 1
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)?
- 3 (Correct answer)
- 2
- 4
- 1
Correct answer: 3
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?
- x = 3 and x = -3 (Correct answer)
- x = 9 and x = -9
- x = 3 only
- x = 0 and x = 9
Correct answer: x = 3 and x = -3
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)?
- 9 (Correct answer)
- 27
- 3
- 81
Correct answer: 9
h(3) = 3^(3-1) = 3² = 9.
Question 6: If f(x) = |x - 5| + 2, what is the minimum value of f(x)?
- 2 (Correct answer)
- 5
- 0
- 7
Correct answer: 2
The absolute value |x - 5| is always ≥ 0, reaching its minimum of 0 when x = 5. At that point f(5) = 0 + 2 = 2, so the minimum value is 2.
Bluebook SAT Test Bluebook SAT Math: Advanced Functions 1
If f(x) = x² + 6x + 5, which of the following is equivalent to f(x)?