Unit G Summary Questions #9: X-intercepts of Asymptotes

9. Describe how to find the x-intercepts of a rational function. Include both the long way and the shortcut way, and why it makes mathematical sense.

To find the x-intercept(s) of an asymptote we use the phrase Y=0! We plug in zero for the y-value using the factored equation. After doing this we multiply both sides by the denominator to eliminate it or we can also use cross multiplying. We then use the resulting equation and solve for the x-values. It may me that there is more than one x-intercept or none at all. The shortcut to solve for the x-intercept is to simply get the factored numerator and solve each factor individually.  It makes sense to this because when we set y to zero and multiply by the denominator on both sides we still end up with the numerator being our equation to solve because anything multiplied by zero basically cancels out.