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.

"X-intercept.. y=0!" To find the x-intercepts of a rational function, plug in zero for y. You must plug in zero for y in the simplified equation. The long way for solving the x-intercept of a rational function is by multiplying both sides by the denominator and solving it. The shortcut is to just equal the top of the rational function (numerator) equal to zero and solve. This makes sense as when you solve it the long way, the denominator is cancelled out.. which leaves you with a numerator equal to zero (the same as the shortcut way).