Real Functions

Pure Mathematics — Second Secondary

Testing a function: the vertical line test

To check whether a drawn graph represents a function, draw a vertical line (parallel to the y-axis) at any position.
If the line meets the graph in at most one point for every position, the relation is a function.
If some vertical line meets it in two or more points, it is not a function.
Example the relation x² + y² = 9 (a circle of radius 3) is not a function, because the vertical line x = 1 meets it at the two points (1, √8) and (1, −√8).
The relation y = x² − 4 is a function, because each value of x gives exactly one value of y.

Real Functions · 2 / 6