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SAT Math: Functions and Function Notation (Drill 3)

Drill 3 · Math · Functions and Function Notation

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About This Drill

SAT Math: Functions and Function Notation (Drill 3) is a Math practice drill covering Functions and Function Notation. It contains 5 original questions created by Brian Stewart, a Barron's test prep author with over 20 years of tutoring experience.

SAT function questions cover evaluating functions, determining domain and range, composing functions, and interpreting transformations on graphs. This drill includes questions where functions are defined by tables, graphs, or algebraic rules.

Questions & Explanations

Question 1. If f(x) = 3x² − 2x + 1, what is f(−2)?

  • A) 9
  • B) 13
  • C) 17 ✓
  • D) 21

Explanation: f(−2) = 3(4) − 2(−2) + 1 = 12 + 4 + 1 = 17.

Question 2. If f(x) = x + 4 and g(x) = 2x − 1, what is g(f(3))?

  • A) 13 ✓
  • B) 9
  • C) 11
  • D) 15

Explanation: f(3) = 7. g(7) = 2(7) − 1 = 13. Work inside out.

Question 3. The graph of y = f(x) is shifted 3 units right and 2 units up. Which equation represents the transformed graph?

  • A) y = f(x + 3) + 2
  • B) y = f(x − 3) + 2 ✓
  • C) y = f(x − 3) − 2
  • D) y = f(x + 3) − 2

Explanation: Right shift by 3: replace x with (x − 3). Up shift by 2: add 2. Result: y = f(x − 3) + 2.

Question 4. What is the domain of f(x) = √x − 5?

  • A) x ≥ 5 ✓
  • B) x > 5
  • C) x ≥ 0
  • D) All real numbers

Explanation: The expression under the square root must be ≥ 0: x − 5 ≥ 0, so x ≥ 5.

Question 5. If f(x) = 4x − 7 and f(a) = 9, what is the value of a?

  • A) 2
  • B) 3
  • C) 4 ✓
  • D) 5

Explanation: 4a − 7 = 9. 4a = 16. a = 4.