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SAT Math

Linear Functions

Linear Functions is a skill in the Algebra domain of the Digital SAT Math section. These are practice questions on it, and each answer choice comes with an explanation of why it is right or wrong.

11 questions. After every answer you’ll see why each choice is right or wrong, not just the one you picked.

Round length
Difficulty (none selected means all)

Sample questions

Open a question to see the answer choices and the correct answer.

If f is the function defined by f(x) = 3x − 7, what is the value of f(6)?
  1. A. 18
  2. B. −3
  3. C. −11
  4. D. 11 ✓

Correct answer: D. Substituting x = 6 gives f(6) = 3(6) − 7 = 18 − 7 = 11.

A water tank is being drained. The tank starts with 480 gallons of water, and the amount of water decreases at a constant rate of 15 gallons per minute. Which equation gives the number of gallons of water, w, remaining in the tank m minutes after the draining begins?
  1. A. w = 480 − 15m ✓
  2. B. w = 480 + 15m
  3. C. w = 15(480)m
  4. D. w = 15m − 480

Correct answer: A. The tank starts at 480 gallons, the constant term, and loses 15 gallons for each minute that passes, so w = 480 − 15m.

Function p models the value, in dollars, of a rare coin t years after it was purchased, where p(t) = 40t + 250. Function q models the value of a different coin; q passes through the points (0, 300) and (5, 450). Which statement correctly compares the two coins' rates of increase in value?
  1. A. Coin q's value decreases over time while coin p's value increases.
  2. B. Coin p's value increases faster per year than coin q's value. ✓
  3. C. Coin q's value increases faster per year than coin p's value.
  4. D. The two coins' values increase at the same rate per year.

Correct answer: B. Coin p increases by $40 per year, the coefficient in p(t) = 40t + 250, while coin q increases by (450 − 300)/(5 − 0) = $30 per year; since $40 is greater than $30, coin p's value increases faster.

A tank is being drained at a constant rate. At t = 3 minutes, the tank holds 64 gallons; at t = 8 minutes, it holds 34 gallons. If V(t) models the volume in gallons after t minutes, what is V(12)?
  1. A. 10 ✓
  2. B. 4
  3. C. 22
  4. D. −14

Correct answer: A. Correct — the rate of change is (34 − 64)/(8 − 3) = −6 gallons per minute; using V(t) = 64 − 6(t − 3) = 82 − 6t, V(12) = 82 − 72 = 10.

If f is a linear function with f(−4) = 11 and f(2) = −7, what is the value of f(5)?
  1. A. −13
  2. B. −16 ✓
  3. C. −10
  4. D. 16

Correct answer: B. Correct — the slope is (−7 − 11)/(2 − (−4)) = −18/6 = −3; using f(2) = −7, f(5) = −7 + (−3)(5 − 2) = −7 − 9 = −16.