y-intercept
In analytic geometry, using the common convention that the horizontal axis represents a variable x and the vertical axis represents a variable y, a y-intercept or vertical intercept is a point where the graph of a function or relation intersects the y-axis of the coordinate system.[1] As such, these points satisfy x = 0.
Using equations
If the curve in question is given as [math]\displaystyle{ y= f(x), }[/math] the y-coordinate of the y-intercept is found by calculating [math]\displaystyle{ f(0). }[/math] Functions which are undefined at x = 0 have no y-intercept.
If the function is linear and is expressed in slope-intercept form as [math]\displaystyle{ f(x)=a+bx }[/math], the constant term [math]\displaystyle{ a }[/math] is the y-coordinate of the y-intercept.[2]
Multiple y-intercepts
Some 2-dimensional mathematical relationships such as circles, ellipses, and hyperbolas can have more than one y-intercept. Because functions associate x values to no more than one y value as part of their definition, they can have at most one y-intercept.
x-intercepts
Analogously, an x-intercept is a point where the graph of a function or relation intersects with the x-axis. As such, these points satisfy y=0. The zeros, or roots, of such a function or relation are the x-coordinates of these x-intercepts.[3]
Unlike y-intercepts, functions of the form y = f(x) may contain multiple x-intercepts. The x-intercepts of functions, if any exist, are often more difficult to locate than the y-intercept, as finding the y intercept involves simply evaluating the function at 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 I-intercept of the current–voltage characteristic of, say, a diode. (In electrical engineering, I is the symbol used for electric current.)
See also
- Regression intercept
References
- ↑ Weisstein, Eric W.. "y-Intercept". MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/y-Intercept.html.
- ↑ Stapel, Elizabeth. "x- and y-Intercepts." Purplemath. Available from http://www.purplemath.com/modules/intrcept.htm.
- ↑ Weisstein, Eric W.. "Root". MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Root.html.
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