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Nonlinear functions — SAT practice questions

Practice 204 Nonlinear functions questions in the app

What this topic is

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.

Sample questions

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Question 1Easier

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?

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Answer: A — −11-11

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

Question 2Easier

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?

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Answer: B — −24-24

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 3Mid

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?

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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.

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Practice 204 Nonlinear functions questions in the app

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