Question

What are the vertical asymptotes for the graph of y = (x + 3)/(x-2)(x+5)?

Answer 1

Hi, Beth,
Mind starting by explaining in your own words what a "vertical asymptote" is and how one finds vertical asymptotes when given a rational function such as y = (x + 3)/(x-2)(x+5)? If you can do that, you've practically answered the question you've posted.

Answer 2

I think a vertical asymptote is the line of the zeroes of the graph? but I'm not 100% sure...
so if I have to find the zeroes it would be 2 and -5, right?

Answer 3

Let me paraphrase what you've typed:

"so if I have to find the zeroes it would be 2 and -5, right?"

would be better as "if I have to find the zeros of the denominator of my rational fraction, they'd be 2 and -5, right?" Right!

Simply write x=2, x=-5, and then you will have specified your vertical asymptotes.

Answer 4

So I don't have to find a zero for the numerator or anything? Just the denominator?

Answer 5

If you're looking for vertical asymptotes alone, then you're done.

If you want to find the zeros of the given function, then you do set the function = to 0 and solve for x.

Answer 6

I hope you'll make up and maintain a glossary of these terms for later study and reference.

VERTICAL ASYMPTOTES of a rational function are found by setting the denominator (only) of the function to zero and solving the resulting equation; write the vertical asymptotes in the form x=a, x=b, and so on.