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Nonlinear functions — SAT practice questions

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Practice 214 Nonlinear functions questions in the app

What this topic is

Quadratic, exponential and polynomial functions make up most of the Nonlinear functions topic.

A quadratic in vertex form, a(x - h)^2 + k, shows its minimum or maximum directly: the value k, reached at x = h. Factored polynomials reveal x-intercepts, since setting each factor equal to zero gives a root. Exponential questions describe growth or decay by a constant percent per period, modeled as an initial amount times a factor such as one minus the rate.

Treating percent decay as subtracting the same amount each time is a frequent confusion, because that describes a linear model. Questions also ask what a constant means in context.

Sample questions

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Question 1Easier

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

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Answer: A — −11

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

Question 2Easier

f(x)=(x+2)(x−1)(x−5)

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

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Answer: B — −24

f(3)=(3+2)(3−1)(3−5)=5⋅2⋅(−2)=−20. Therefore f(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 p percent of its mass each hour, where p is a constant. What is the value of p?

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Answer: C — 20

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

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Practice 214 Nonlinear functions questions in the app

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