SAT · Math · Advanced Math

Nonlinear Functions on the Digital SAT: How to Answer These Questions

Whether you can evaluate, build and interpret quadratic, exponential and other nonlinear functions.

How to answer it

  1. Substitute the input in parentheses.
  2. Apply exponents before multiplying.
  3. Then multiply, add and subtract in order.

Worked example

An original question in the SAT format, already answered.

SAT MathWorked example

f(x) = 2x² − 3

What is the value of f(−2)?

  1. A−11
  2. B−5
  3. C5
  4. D13

Answer: C. f(−2) = 2(−2)² − 3 = 2(4) − 3 = 5. Choice A comes from treating −2² as −4.

The most common trap

Squaring a negative without parentheses. (−2)² is 4, not −4.

Practice it

Hourly Prep’s daily sets mix nonlinear functions with the rest of SAT Math, and send more of it your way when it’s a weak spot. See how the SAT prep plan works, or browse the other SAT skill guides.

Primary sources

Keep going

SAT · Math

Nonlinear Equations and Systems

Solve quadratics by factoring, the quadratic formula or graphing. A system with a line and a parabola can have zero, one or two solutions.

Read the guide →
SAT · Math

Equivalent Expressions

Rewrite expressions by expanding, factoring or combining like terms until the form matches a choice.

Read the guide →

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