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Nonlinear functions — SAT practice questions

Nonlinear functions on the SAT Math section cover polynomials, quadratics, and exponential models rather than straight lines. Students must evaluate a given equation at an input, find a minimum from vertex form, and determine a constant percent change in a decay setting. The exam typically defines a function and then asks for one numeric result, such as a minimum value or the constant p. Answers are usually a single number. Common traps include skipping a last arithmetic step, mixing up the vertex with an intercept, and treating remaining mass as the percent lost each hour.

  • Section: Math 44 questions on the paper
  • 204 practice questions in the app

Sample questions

Question 1

The function ff is defined by f(x)=2(x−5)2−11f(x) = 2(x - 5)^2 - 11. What is the minimum value of ff?

  1. A-11
  2. B-5
  3. C2
  4. D5
Show answer

Answer: A — -11

Because the squared term is always at least 0 and the leading coefficient is positive, the minimum occurs when x=5x = 5 and equals -11.

Question 2

f(x)=(x+2)(x−1)(x−5)f(x) = (x + 2)(x - 1)(x - 5)

The function ff is defined by the given equation. What is the value of f(3)−4f(3) - 4?

  1. A-28
  2. B-24
  3. C-20
  4. D-16
Show answer

Answer: B — -24

f(3)=(3+2)(3−1)(3−5)=5⋅2⋅(−2)=−20f(3) = (3+2)(3-1)(3-5) = 5 \cdot 2 \cdot (-2) = -20. Therefore f(3)−4=−24f(3) - 4 = -24.

Question 3

A substance has an initial mass of 250 grams. After 2 hours, the mass of the substance is 160 grams. The substance loses pp percent of its mass each hour, where pp is a constant. What is the value of pp?

  1. A10
  2. B15
  3. C20
  4. D25
Show answer

Answer: C — 20

The ratio of the 2-hour mass to the initial mass is 160250=0.64\dfrac{160}{250}=0.64. The hourly retention factor is 0.64=0.8\sqrt{0.64}=0.8, so the mass decreases by 20%20\% each hour and p=20p=20.

Practice 204 Nonlinear functions questions in the app

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