Answer
As many as the power of an exponent (2 for an $x^2$ function, 3 for an $x^3$ function, and so on)
Work Step by Step
A linear function ($y=x+b$) has at most one x-intercept. A parabolic function ($y=x^2$) has at most two x-intercepts. Using this pattern, a cubic function ($y=x^3$) has at most three x-intercepts. As we increase the power of the exponent, we increase the maximum number of x-intercepts.
Thus, there could be as many x-intercepts as the power of the exponent.
