In Exercises 21–36, find the vertical asymptotes, if any, and the...

Question

In Exercises 21–36, find the vertical asymptotes, if any, and the values of x corresponding to holes, if any, of the graph of each rational function. f(x)=(x^2−9)/(x−3)

Accepted Answer

consider the given rational function and find vertical ascent owes and vise of X corresponding to holtz. So my equation is X squared minus 49 over X plus seven. I want to find any dis continuity in this rational function to do that you would normally set as an on air equal to zero and solve for X. However we want to check for specific kinds of discontinuities. So I'm gonna find a first class until in our whole let's go ahead and factor out our numerator that will help us figure out our classification of this continuity. So on the top we actually have a difference of two squares. We call difference of two squares. It tells us that we have a difference of two squares like this X squared minus 49. It will be X plus seven Which is a square to 49. X - said that is defined by X plus seven. So no, we will have a hole in our graph if we have a common factor on both the numerator and the denominator. If you notice here we have an X plus seven both on the top and on the bottom. Because those are common factors. Our whole what happened at X for certain. So let's go ahead and simplify this function to see if we get a vertical aceto really simplify expo sevens on top, expo sevens on the bottom we just get x minus seven at the end X -7 doesn't have a dis continuity. So we actually have no vertical essence. So we know we have no bro class until let's look at our whole to find what our whole is. We're gonna set this equation X plus seven equal to zero and then solve for X. Track seven. We get x equals -7. So our whole happens at X equals negative seven. And we have no vertical as minto or she needs to answer to our problem as answers. See? Okay, I hope to help you solve the problem. Thank you for watching. Goodbye.

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In Exercises 21–36, find the vertical asymptotes, if any, and the values of x corresponding to holes, if any, of the graph of each rational function. f(x)=(x^2−9)/(x−3)