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SAT Math: Functions and Function Notation (Drill 2)

Drill 2 · Math · Functions and Function Notation

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About This Drill

SAT Math: Functions and Function Notation (Drill 2) 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, identifying domain and range, composing functions, and interpreting function notation. This drill includes table-based functions, piecewise notation, and reading the output of composite expressions.

Questions & Explanations

Question 1. The function f(x) = (x + 2)/(x − 3) is defined for all real numbers except which value of x?

  • A) x = −2
  • B) x = 2
  • C) x = 3 ✓
  • D) x = −3

Explanation: A rational function is undefined where the denominator equals zero: x − 3 = 0, so x = 3.

Question 2. If f(x) = 2x − 1, which of the following is equal to f(a + 3)?

  • A) 2a + 5 ✓
  • B) 2a + 2
  • C) 2a + 3
  • D) 2a − 1

Explanation: f(a + 3) = 2(a + 3) − 1 = 2a + 6 − 1 = 2a + 5.

Question 3. If g(x) = x² + 2, how many values of x satisfy g(x) = 27?

  • A) One
  • B) Two ✓
  • C) Three
  • D) Zero

Explanation: x² + 2 = 27 → x² = 25 → x = 5 or x = −5. Two values.

Question 4. If f(x) = x² and g(x) = x − 4, what is the value of g(f(3))?

  • A) −1
  • B) 1
  • C) 3
  • D) 5 ✓

Explanation: f(3) = 9. Then g(9) = 9 − 4 = 5.

Question 5. What is the range of the function f(x) = |x| + 3?

  • A) f(x) ≥ 3 ✓
  • B) f(x) ≥ 0
  • C) All real numbers
  • D) f(x) > 3

Explanation: |x| ≥ 0, so |x| + 3 ≥ 3. The minimum is 3 at x = 0. Choice D excludes 3, but f(0) = 3 is in the range.