Non Linear Functions
Interpreting nonlinear graphs, creating equations, and understanding transformations
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You get a parabola, an exponential, or a transformation. The question asks: what does this function do?
Why this matters
Nonlinear functions appear constantly on the Digital SAT. Most students can plug in numbers but freeze when asked to interpret a graph, pick the right model, or describe a transformation. There are five specific question types here, and each one tests a different skill. Recognize the type and you know exactly what to do.
The five patterns
Features of Graphs
Read a nonlinear graph — parabola, exponential, or other — and interpret key features like intercepts, vertex, or maximum in context.
›Create Equations
Turn a real-world scenario into a nonlinear equation and solve it. The hard part isn't the math — it's building the equation correctly.
›Evaluation of Functions
Plug in values, find the vertex, or rewrite a function in a different form. Pure function manipulation — no context, just algebra.
›Identify Models
Given a real-world scenario with growth or decay, decide whether a linear, quadratic, or exponential model fits best.
›Function Transforms
Know how replacing x with (x − h) or adding k shifts, stretches, or reflects a graph. The rules are simple but easy to reverse.
The biggest trap: mixing up horizontal and vertical transformations. Adding 3 inside the function shifts left, not right. Adding 3 outside shifts up. The SAT deliberately exploits this confusion.