Final answer:
To find the x-intercept of a rational function, set the numerator equal to zero and solve for x, as the x-intercept is where the function intersects the x-axis (y=0).
Step-by-step explanation:
To find the x-intercept in rational functions, set the numerator of the rational function equal to zero and solve for x. This is because the x-intercept is the point(s) where the function crosses the x-axis, at which the value of y is zero. If the function is given in a different format, you may need to rearrange or manipulate it to identify the numerator.
For example, if we have a rational function of the form f(x) = (ax + b) / (cx + d), we'd set ax + b = 0 and solve for x. If a and b are real numbers and a is not zero, then the x-intercept can be found by calculating x = -b/a. If the rational function cannot be easily rearranged to isolate x, one may employ methods such as factoring or the use of the quadratic formula for polynomials to find the x-intercepts.