What is the x-intercept of a graph?

The x-intercept of a graph is defined as the x-coordinate of the point where the graph crosses the x-axis. At this intersection, the value of y is zero, which is the defining characteristic of an x-intercept. When finding the x-intercept, one typically sets the equation of the graph equal to zero and solves for the value of x. This is a fundamental concept in graph interpretation and function analysis, as the x-intercept helps to reveal important information about the function's behavior and root locations.

In contrast, the y-intercept corresponds to the y-coordinate at which the graph crosses the y-axis, addressing a different component of the graph. A point where the slope is zero refers to a horizontal tangent, which may indicate a local maximum or minimum, but not specifically to an intercept. Lastly, a location where the function is undefined does not directly relate to intercepts but rather to points where the function cannot take on a value. Thus, identifying the x-intercept as the x-coordinate at the point of intersection with the x-axis is crucial for understanding graph characteristics and behavior.