Bluebook SAT Math: Advanced Functions Questions and Answers 3 — Questions and Answers
Question 1: If f(x) = |2x - 6|, for how many values of x does f(x) = 4?
- 0
- 1
- 2 (Correct answer)
- 3
Correct answer: 2
|2x-6|=4 gives 2x-6=4 (x=5) or 2x-6=-4 (x=1), so there are exactly 2 solutions.
Question 2: The function p(x) = x⁴ - 5x² + 4. How many real zeros does p(x) have?
- 0
- 2
- 4 (Correct answer)
- 6
Correct answer: 4
Let u=x²: u²-5u+4=(u-1)(u-4)=0 gives x=±1 or x=±2, yielding 4 real zeros.
Question 3: If f(x) = (x+1)/(x-1), what is f(f(x))?
- x (Correct answer)
- 1/x
- -x
- (x+1)/(x-1)
Correct answer: x
Replacing x with (x+1)/(x-1) and simplifying the compound fraction yields f(f(x)) = x.
Question 4: For f(x) = 2^x, which transformation produces g(x) = 2^(x+3) - 4?
- Shift left 3, down 4 (Correct answer)
- Shift right 3, down 4
- Shift left 3, up 4
- Shift right 3, up 4
Correct answer: Shift left 3, down 4
Adding 3 inside the exponent shifts the graph left 3 units; subtracting 4 outside shifts it down 4 units.
Question 5: If f is an odd function and f(3) = -5, what is f(-3)?
- -5
- 5 (Correct answer)
- 0
- Cannot be determined
Correct answer: 5
For an odd function f(-x) = -f(x), so f(-3) = -f(3) = -(-5) = 5.
Question 6: The function f(x) = a(x - 2)² - 3 passes through the point (0, 1). What is the value of a?
- 1 (Correct answer)
- 2
- 3
- 4
Correct answer: 1
Substitute (0, 1): 1 = a(0-2)² - 3 = 4a - 3, so 4a = 4 and a = 1.
Bluebook SAT Math: Advanced Functions Questions and Answers 3
If f(x) = |2x - 6|, for how many values of x does f(x) = 4?