SAT Math Practice
Nonlinear Functions
Evaluate quadratic and exponential functions, and model real-world growth and decay scenarios.
94 original nonlinear functions questions in the SAT Ranker bank, with instant scoring and an Elo-based rank once you sign up. Below are a few free samples with full explanations.
Sample question 1 · medium
If f(x) = 2x² − 3, what is f(−2)?
-11
1
✓ 5
8
f(−2) = 2(−2)² − 3 = 2(4) − 3 = 8 − 3 = 5.
Sample question 2 · hard
A population of bacteria doubles every 3 hours. If the population starts at 200, what is the population after 9 hours?
400
800
✓ 1600
3200
9 hours is 3 doubling periods (9 ÷ 3). Population = 200 × 2³ = 200 × 8 = 1600.
Sample question 3 · easy
If f(x) = 1x² - 9, what is f(1)?
-6
✓ -8
8
-7
f(1) = 1(1)² - 9 = 1(1) - 9 = -8.
Sample question 4 · easy
If f(x) = -2x² + 7, what is f(-1)?
✓ 5
6
-5
9
f(-1) = -2(-1)² + 7 = -2(1) + 7 = 5.
Sample question 5 · easy
If f(x) = 2x² - 4, what is f(2)?
✓ 4
0
12
-4
f(2) = 2(2)² - 4 = 2(4) - 4 = 4.
More topics
SAT Math skills
Linear Equations in One VariableLinear Equations in Two VariablesLinear FunctionsLinear InequalitiesSystems of Linear EquationsEquivalent ExpressionsNonlinear Equations and SystemsRatios, Rates, Proportions, and UnitsPercentagesOne-Variable DataTwo-Variable DataProbabilitySample Statistics and Margin of ErrorEvaluating Statistical ClaimsRight Triangles and TrigonometryCirclesArea and VolumeLines, Angles, and Triangles