Question

State the horizontal asymptote of the rational function.
f(x) = (x+9) / (x^2+2x+3)

Answer 1

@amistre64 @hartnn @Hero

Answer 2

The horizontal asymptote will be found where there is a 0 in the numerator. For what value x does the numerator = 0?

Answer 3

-9

Answer 4

Horizontal is a "y = " line, while verrtical is an "x = " line. In a rational function, the y goes on the top for the rise of the function whereas the x goes on the bottom for the run of the function. Thats how you know that the horizontal asymptote is in the numerator. If it was in the denominator, it would be undefined where x = 0 becasue you are not allowed to have a 0 as a denominator, right?

Answer 5

And you are correct...the horizontal asymptote is at y = -9

Answer 6

That's what I thought but my choices are
y = x

None

y = 0

y = 9

Answer 7

ok, then let's look at the function as a whole. If you can factor the denominator and one of its factors is x + 9, they would cancel each other out and then the answer would be "none". Let's look.

Answer 8

Well,,,the denominator has zeros at\[-1\pm i \sqrt{2}\]So that's not going to work. Let me dwell on this for a tiny bit, ok?

Answer 9

Is it possible that there's a typo? I took this test a while ago but I got this question wrong... I think I'll go with 9 (fingers crossed it's a typo)

Answer 10

Do you think you could help with one more? I did half of it but I can't get the rest

Answer 11

Okk, no there's no typo. I forgot my rules for the horizontal asymptotes...it's been a while! But here they are:

Answer 12

Look at your numerator. It has a one degree polynomial in it, meaning that x is raised to the first power:\[x ^{1}=x\]The denominator however, has an x raised to the second power\[x ^{2}\]The rule is that if the x power in the numerator is less than the x power in the denominator, then the horizontal asymptote is the x axis, or y = 0.

Answer 13

ohhhh okay! Thank you sooooo much!

Answer 14

can you help with one more?

Answer 15

i can certainly try!

Answer 16

More like just checking this one cause I think I fiugred it out...

Answer 17

Give an example of a rational function that has a horizontal asymptote at y = 0 and a vertical asymptote at,
x = 2 and x = 1.

I put

x+4
--------
x^2-3x+2

Answer 18

Here are your rules in a nutshell:\[f(x)=\frac{ ax ^{n}+... }{ bx ^{m}+... }\]If n<m, the horizontal asymptote is the x axis or y = 0 line. If n = m, the horizontal asymptote is the line y = a/b (a and b come from your coeffiecients in your polynomials). If n>m, there is no horizontal asymptote. See that? Write that down for future reference...it always applies!

Answer 19

That's very good! You're correct!

Answer 20

Awesome! Thanks!

Answer 21

You are very welcome!

Answer 22

It was a good refresher for me...I had forgotten those, too! Now I won't forget again! So I should also be thanking you!