Y-intercept

Multiple y {\displaystyle y} -intercepts

Some 2-dimensional mathematical relationships such as circles, ellipses, and hyperbolas can have more than one ${\displaystyle y}$-intercept. Because functions associate ${\displaystyle x}$-values to no more than one ${\displaystyle y}$-value as part of their definition, they can have at most one ${\displaystyle y}$-intercept.

x {\displaystyle x} -intercepts

Analogously, an ${\displaystyle x}$-intercept is a point where the graph of a function or relation intersects with the ${\displaystyle x}$-axis. As such, these points satisfy ${\displaystyle y=0}$. The zeros, or roots, of such a function or relation are the ${\displaystyle x}$-coordinates of these ${\displaystyle x}$-intercepts.

Functions of the form ${\displaystyle y=f(x)}$ have at most one ${\displaystyle y}$-intercept, but may contain multiple ${\displaystyle x}$-intercepts. The ${\displaystyle x}$-intercepts of functions, if any exist, are often more difficult to locate than the ${\displaystyle y}$-intercept, as finding the ${\displaystyle y}$-intercept involves simply evaluating the function at ${\displaystyle x=0}$.

In higher dimensions

The notion may be extended for 3-dimensional space and higher dimensions, as well as for other coordinate axes, possibly with other names. For example, one may speak of the ${\displaystyle I}$-intercept of the current–voltage characteristic of, say, a diode. (In electrical engineering, ${\displaystyle I}$ is the symbol used for electric current.)