Editing Horizontal line test (section)

==In calculus==
A ''horizontal line'' is a straight, flat line that goes from left to right. Given a function <math>f \colon \mathbb{R} \to \mathbb{R}</math> (i.e. from the [[real numbers]] to the real numbers), we can decide if it is [[injective]] by looking at horizontal lines that intersect the function's [[graph of a function|graph]]. If any horizontal line <math>y=c</math>  intersects the graph in more than one point, the function is not injective. To see this, note that the points of intersection have the same y-value (because they lie on the line <math>y=c</math>) but different x values, which by definition means the function cannot be injective.<ref name="Stewart"/>

{| border="1"
|-
| align="center"|[[Image:Horizontal-test-ok.png]]<br>
Passes the test (injective)
| align="center"|[[Image:Horizontal-test-fail.png]]<br>
Fails the test (not injective)
|}

Variations of the horizontal line test can be used to determine whether a function is [[surjective]] or [[bijective]]:
*The function ''f'' is surjective (i.e., onto) [[if and only if]] its graph intersects any horizontal line at '''least''' once.
*''f'' is bijective if and only if any horizontal line will intersect the graph '''exactly''' once.