SAT and ACT math terms · SAT Math, ACT Math
Linear function
Linear function: A function whose graph is a straight line, with a constant rate of change, written f(x) = mx + b.
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What it means
In a linear function, equal changes in x always produce equal changes in y. In a table, the differences between consecutive y-values (for evenly spaced x-values) are constant.
Linear models describe situations with a constant rate, such as a fixed hourly wage or steady speed.
Example
In the table x: 0, 1, 2, 3 and y: 5, 8, 11, 14, y increases by 3 each time, so f(x) = 3x + 5.
On the exam
The SAT tests linear functions heavily in the Algebra domain, often asking you to build or interpret a model.
Lessons and practice questions
Related terms
- SlopeThe rate of change of a line: how much y changes for each one-unit increase in x, calculated as rise over run.
- Exponential growth and decayChange by a constant percentage or factor per time period, modeled by y = a(1 + r)ᵗ for growth or y = a(1 − r)ᵗ for decay.
- Function notationWriting f(x) to show the output of function f for input x.