Question

How do I find the asymptotes for y=[5/(x-3)]+2?

Answer 1

Welcome, and congrats on asking your first question!

Answer 2

@shania0703 Thanks! Can you help me?

Answer 3

A vertical asymptote occurs for x values yielding undefined results. What x value would make the function undefined?

Answer 4

If x equals 3, x-3=0 and 5/0=0

Answer 5

Good.

Now to find any horizontal asymptotes, let x get very large (tend to infinity.)

What happens to the rational (fraction) expression when x gets very large?

Answer 6

When x gets large, the rational expression also gets large.

Answer 7

Actually, it gets smaller. As the denominator of a fraction increases with the numerator constant, the value of the fraction gets smaller.

Consider:
\[\frac{ 5 }{ 8-3 }=1\]
\[\frac{ 5 }{ 8000000-3}\approx .0000006\]
For a horizontal asymptote you let x tend to infinity and see what the functions value gets closer to.

As the fraction gets closer to zero, the graph of the function gets closer to its horizontal asymptote.

Answer 8

Oh... That makes sense! I use this fact to find the asymptotes of my equation?

Answer 9

Yes. What value does y get closer to as the fraction goes toward zero?

Answer 10

Y gets closer to 2.

Answer 11

There's your horizontal asymptote.

Answer 12

So my vetical asymptote is 3 and my horizontal asymptote is 2? This makes so much sense! Thank you very much!

Answer 13

That's a pretty rough graph.

You're welcome.