Bluebook SAT Test Bluebook SAT Math: Advanced Functions Questions and Answers 3 — Questions and Answers
Question 1: The function f(x) = (x - 1)(x + 3) has x-intercepts at:
- x = 1 and x = -3 (Correct answer)
- x = -1 and x = 3
- x = 1 and x = 3
- x = -1 and x = -3
Correct answer: x = 1 and x = -3
Setting each factor to zero: x - 1 = 0 gives x = 1, and x + 3 = 0 gives x = -3.
Question 2: If f(x) = √(x + 4), what is the domain of f?
- x ≥ -4 (Correct answer)
- x > -4
- x ≥ 4
- all real numbers
Correct answer: x ≥ -4
The radicand must be non-negative: x + 4 ≥ 0, so x ≥ -4.
Question 3: A function f satisfies f(2) = 5 and f(5) = 11. If f is linear, what is f(8)?
- 17 (Correct answer)
- 14
- 19
- 22
Correct answer: 17
The slope is (11-5)/(5-2) = 2, so each step of 3 adds 6; f(8) = 11 + 6 = 17.
Question 4: If g(x) = x² + bx + c has a vertex at (3, -4), what is the value of b?
- -6 (Correct answer)
- 6
- -3
- 3
Correct answer: -6
The vertex x-coordinate is -b/(2a) = 3, so -b/2 = 3, giving b = -6.
Question 5: For f(x) = |x - 2| + 1, which statement is true?
- The minimum value of f is 1 (Correct answer)
- The minimum value of f is 0
- f has no minimum
- The minimum value of f is 2
Correct answer: The minimum value of f is 1
Since |x - 2| ≥ 0, the minimum occurs when |x - 2| = 0 (at x = 2), giving f(2) = 1.
Question 6: If f(x) = 2x - 4 and g(x) = x/2 + 2, then f(g(x)) =
- x (Correct answer)
- 2x
- x - 2
- 4x - 4
Correct answer: x
f(g(x)) = 2(x/2 + 2) - 4 = x + 4 - 4 = x, showing g is the inverse of f.
Question 7: Which transformation maps y = x² onto y = (x + 2)² - 5?
- Shift left 2, down 5 (Correct answer)
- Shift right 2, down 5
- Shift left 2, up 5
- Shift right 2, up 5
Correct answer: Shift left 2, down 5
Replacing x with (x + 2) shifts left 2; subtracting 5 shifts down 5.
Bluebook SAT Test Bluebook SAT Math: Advanced Functions Questions and Answers 3
The function f(x) = (x - 1)(x + 3) has x-intercepts at: