What is the outcome of a graph crossing the x-axis?

When a graph crosses the x-axis, it indicates the points where the function has an output of zero. These points are known as x-intercepts. At these intersections, the value of y is zero, which means that the corresponding x-value represents a solution to the equation of the function set equal to zero. This is significant in algebra and calculus, as it helps in understanding the behavior of the function in relation to the x-axis and can also give insights into the roots of the function.

In contrast, the other options pertain to different concepts. The y-intercept refers to the point where a graph intersects the y-axis and is not related to crossing the x-axis. An undefined slope typically refers to a vertical line, which does not cross the x-axis in the context of functions. The statement that the function has no solutions is incorrect because crossing the x-axis explicitly indicates that there are solutions (the x-values are solutions where the output is zero). Hence, crossing the x-axis is directly related to identifying x-intercepts of the function.