By Marie Mulrooney, Updated August 30, 2022
A function describes a relationship in which each input corresponds to exactly one output. Think of a classroom: the first set is students, the second set is their grades. Each student receives a single grade, even if several students share the same score.
To verify whether an equation defines a function, graph it and apply the vertical line test. The following steps guide you through the process.
Draw the graph on coordinate paper. For linear equations, plot two or more points and join them with a straight line. For other forms, identify characteristic shapes or compute multiple points: choose an x‑value, calculate the corresponding y, and plot the point. Repeat to reveal the overall shape.
Draw a vertical line that passes through any point on your graph. If the line intersects the graph at more than one point, the equation is not a function.
Extend the vertical line across the entire range of the graph. If it ever meets the curve or line at more than one location, the equation fails the test and cannot be considered a function. If it never intersects more than once, the equation represents a function.
