Unit G Summary Question #9: X-intercepts of a rational function

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

To find the x intercepts, we remember x-intercept...Y=0! So, we replace y with 0. One way you can find the x-intercept is the long way, you use the simplified equation and set y=0 and then multiply by a common denominator, which cancels out the denominator. Another way to look at it, is cross multiplying. When you cross multiply, your y is 0 and the denominator cancels out so you are left with 0= the numerator. However, since the denominator is always being cancels out we can just set the top equal to 0. This is the shortcut way and makes sense because the denominator is canceled every time.