Question

can someone explain to me how to find the asymptotes of a function

Answer 1

You have to use infinite limits, you're in Cal 1 right?

Answer 2

no I;m in algebra 2

Answer 3

Gotcha, then the concept is a little different. For a vertical asymptote, you have to find the values where the function is un-defined. For a horizontal asymptote it's much easier to use a calculus technique called limits, so for this function it would be -3. The way to do it in algebra involves comparing the degrees of the terms in a rational function, for this function you have to alter it a little bit. Give me a second to write it out

Answer 4

Let me know if that makes sense.

Answer 5

Sure, just start a thread

Answer 6

This one is almost identical to the one we just did, it actually has the exact same answer believe it or not.

Answer 7

I know

Answer 8

I got -3 as the asymptote when I drew a line on the graph

Answer 9

It can be, but for most functions it might be hard to see exactly. It's best to use the techniques to solve for it. That's correct, what about the vertical asymptote?

Answer 10

0

Answer 11

Correct

Answer 12

how about the domain and range?

Answer 13

the HA= 3?

Answer 14

VA = 0
HA = -3

Answer 15

ooh okay I get it

Answer 16

Remember that the domain is all of the x values for which the function is defined. The range is simply the y values where the function is defined. So in this case:

Domain: \[[-\infty,\infty] \rightarrow x \neq0\]
Range: \[[-\infty,\infty] \rightarrow y \neq-3\]

Answer 17

I set it up so that the leading term of the numerator was the one with the highest power, that makes it easier to see when you are comparing degrees and coefficients of terms.

Answer 18

okay thank you so much :)

Answer 19

You're welcome, good luck!