Question

what would be the end behavior of f(x)2x^2-5x-10/2x^2-20

Answer 1

@Hero e.e

Answer 2

\[f(x)\frac{ 2x^2-5x-10 }{ 2x^2-20}\]

Answer 3

That's better

Answer 4

First factor and simplify the expression, then apply the limit as \(x \to \infty\) of \(f(x)\)

Answer 5

Also apply the limit as \(x \to\) the vertical asymptote

Answer 6

By \(\infty\) I am implying \(\pm \infty\)

Answer 7

this is just a practice problem. They sent a video for us to watch so we could learn and it made no sense. I just need to know what I need to do then I could figure it all out.

Answer 8

It's okay thank you Hero

Answer 9

In this case, you need to find the vertical asymptote by setting the denominator equal to zero and solving for \(x\). Then apply the limit as \(x\) approaches the asymptote.

Answer 10

Then you apply the limit again as \(x \to \pm \infty\) to find the horizontal asymptotes

Answer 11

by chance is the vertical asymptote \[x=\pm \sqrt{10}\] ? or did I do that completely wrong lol

Answer 12

Correct

Answer 13

Now find the limit as \(x \to \pm \sqrt{10}\)

Answer 14

and how do you do that? that was the farthest I actually got how to do.

Answer 15

You apply the limit laws for the function. You have to apply it at least six times in this case because you have two vertical asymptotes and two horizontal asymptotes.

Answer 16

So you have to find each of these:
$$\lim_{x \to \sqrt{10}^+}f(x)$$$$\lim_{x \to \sqrt{10}^-}f(x)$$$$\lim_{x \to -\sqrt{10}^-}f(x)$$$$\lim_{x \to -\sqrt{10}^+}f(x)$$$$\lim_{x \to -\infty}f(x)$$$$\lim_{x \to \infty}f(x)$$

Answer 17

then after that what would I do?

Answer 18

You're done after that.

Answer 19

oh okay thank you hero!

Answer 20

Are you sure you know how to find them?

Answer 21

I'll be able to figure it out I have to go anyways. But thank you for the help.

Answer 22

Okay, good luck