Bluebook SAT Test Bluebook SAT Math: Advanced Functions Questions and Answers 2 — Questions and Answers
Question 1: If f(x) = x² - 4x + 7, what is the minimum value of f(x)?
- 3 (Correct answer)
- 7
- -4
- 2
Correct answer: 3
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))?
- 16
- 8
- 256 (Correct answer)
- 32
Correct answer: 256
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 =
- 3 (Correct answer)
- 6
- -3
- 0
Correct answer: 3
Set 2x - 6 = 0, giving x = 3.
Question 4: If f(x) = 3x + 1 and g(x) = x², what is f(g(x))?
- 3x² + 1 (Correct answer)
- 9x² + 1
- (3x+1)²
- 3x + x²
Correct answer: 3x² + 1
f(g(x)) = f(x²) = 3(x²) + 1 = 3x² + 1.
Question 5: Which of the following is an even function?
- f(x) = x⁴ - 2x² (Correct answer)
- f(x) = x³ + x
- f(x) = x² + x
- f(x) = x⁵
Correct answer: f(x) = x⁴ - 2x²
A function is even if f(-x) = f(x); f(x) = x⁴ - 2x² satisfies this since all exponents are even.
Question 6: If the graph of y = f(x) is shifted 3 units to the right, the new equation is:
- y = f(x - 3) (Correct answer)
- y = f(x + 3)
- y = f(x) - 3
- y = f(x) + 3
Correct answer: y = f(x - 3)
A horizontal shift right by 3 units is given by replacing x with (x - 3).
Question 7: The inverse of f(x) = 5x - 2 is:
- f⁻¹(x) = (x + 2)/5 (Correct answer)
- f⁻¹(x) = (x - 2)/5
- f⁻¹(x) = 5x + 2
- f⁻¹(x) = 1/(5x - 2)
Correct answer: f⁻¹(x) = (x + 2)/5
Swap x and y: x = 5y - 2, then solve for y: y = (x + 2)/5.
Bluebook SAT Test Bluebook SAT Math: Advanced Functions Questions and Answers 2
If f(x) = x² - 4x + 7, what is the minimum value of f(x)?