Unit G Summary #9: X-Intercept

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 of a rational function, f(x) will be y and I will set it equals to 0 because x-intercepts always have the y-value equal 0. I will divide both sides by the denominator. Because y=0 which means that the denominator multiplies with y will equal 0. So I will have the numerator equals to 0, then I solve for x. It is a long way to do it. However, I learn the pattern and figure out there is a shortcut. I can just put the numerator equals to 0 right away without dividing the denominator. The shortcut makes mathematical sense because anything divides or multiplies with 0 will be 0. So in any problems, the other side, where the y=0, will always remain as 0 when I look for the x-intercepts.