The x-intercept of a graph of a function

x-axis, or the point(s) of the graph for which \(f(x) = 0\).

*f*represented in a Cartesian plane is the name given to the x-coordinate of each of the points where the graph of*f*intersects with thex-axis, or the point(s) of the graph for which \(f(x) = 0\).

The expression “

*x-intercept*” can also indicate each of the points where the line of a function intersects with the x-axis. It consists of points for which the x-coordinate is zero.The x-coordinates of these points are also called the zeros of the function *f*.

### Example

- A line only has one x-intercept.

- Some curves have 0, 1, 2, 3, … x-intercepts.
This second-degree polynomial function has two x-intercepts, which are when \( x = -8 \) or

*x*= 2. These two values are also the zeros of the function defined by \(f(x) = 0.5 (x + 8)(x – 2)\). These are the two points where the graph of the function crosses the x-axis.

- Theoretically, this graph has an infinite number of x-intercepts: