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SAT Math: Functions and Function Notation (Drill 1)

Drill 1 · Math · Functions and Function Notation

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About This Drill

SAT Math: Functions and Function Notation (Drill 1) is a Math practice drill covering Functions and Function Notation. It contains 5 original questions developed by Brian Stewart, a Barron's test prep author with over 20 years of tutoring experience.

SAT function questions test your ability to evaluate functions for given inputs, interpret function notation, work with composite functions, determine domain and range, and read function behavior from graphs. This drill covers both algebraic and graphical representations.

Questions & Explanations

Question 1. If f(x) = 3x² − 2x + 1, what is the value of f(4)?

  • A) 37
  • B) 41 ✓
  • C) 45
  • D) 49

Explanation: Substitute x = 4: f(4) = 3(4)² − 2(4) + 1 = 3(16) − 8 + 1 = 48 − 8 + 1 = 41.

Question 2. If g(x) = 5x − 7, for what value of x does g(x) = 18?

  • A) 2
  • B) 3
  • C) 4
  • D) 5 ✓

Explanation: Set g(x) = 18: 5x − 7 = 18. Add 7: 5x = 25. Divide by 5: x = 5.

Question 3. If f(x) = x + 3 and g(x) = 2x, what is the value of f(g(4))?

  • A) 11 ✓
  • B) 14
  • C) 10
  • D) 7

Explanation: Work from the inside out. First compute g(4) = 2(4) = 8. Then compute f(8) = 8 + 3 = 11. Note that f(g(4)) ≠ g(f(4)); order matters in composition.

Question 4. The function f(x) = √x − 5 is defined for all x in its domain. What is the domain of f?

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

Explanation: The expression under a square root must be non-negative: x − 5 ≥ 0, so x ≥ 5. Choice B (x > 5) excludes x = 5, but f(5) = √0 = 0 is defined. The domain is x ≥ 5.

Question 5. A factory's daily production cost, in dollars, for manufacturing n items is modeled by C(n) = 15n + 200. What does the value C(0) = 200 represent?

  • A) The cost of producing 200 items
  • B) The cost per item
  • C) The number of items that can be produced for $200
  • D) The fixed daily cost before any items are produced ✓

Explanation: C(0) represents the cost when n = 0 items are produced. Since C(0) = 15(0) + 200 = 200, this is the fixed daily cost the factory incurs regardless of production. The coefficient 15 represents the variable cost per item.