The x-intercept of a graph of a function 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 the
x-axis, or the point(s) of the graph for which \(f(x) = 0\).
x-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:
