Question

State the horizontal asymptote of the rational function.
f(x) = x + 9 / x^2 + 8x + 8

Answer 1

There is a rule for horizonal asymptotes, related to the degree of the num'r vs. the degree of the den'r. Does that sound familiar?

Answer 2

Yes, so it is horizontal because the denominator is bigger than the numerator

Answer 3

One way of viewing it is to plug in a very large number x :) and evaluate

Answer 4

Well, that isn't what makes it a HORIZONTAL asymptote. There are 2 cases where you get a horizontal asymyptote:

deg num'r < deg den'r
deg num'r = deg den'r

Answer 5

(x + 9) / (x^2 + 8x + 8) just pick x= 999

Answer 6

This is the first of those, so it gives a specific result. Think of it this way: for a BIG value of x, the den'r is going to be MUCH BIGGER than the num'r, so it will "take over". What will that do to the value of the rational expression?

Answer 7

Or graphically

https://www.google.com/search?q=(x+%2B+9)+%2F+(x%5E2+%2B+8x+%2B+8)&oq=(x+%2B+9)+%2F+(x%5E2+%2B+8x+%2B+8)&aqs=chrome..69i57.658j0&sourceid=chrome&ie=UTF-8

Just zoom out and scroll to the right and you will zee that the asymptote is... :D

Answer 8

in the previous case the numerator's "degree" was bigger than the denominator's
in this case is the other way around,
notice the degree of the numerator is 1
and the denominator's degree is 2

so you do have a horizontal asymptote, what is it? well, is at y =0, or the x-axis

Answer 9

x/x^2 here is another example

the x^2 will get very big very fast as you aproach big numbers like 100

100/10000 = very small number

1000/1000000= even smaller number and you could say number is so small it aproaches 0

Answer 10

so y = x

Answer 11

well the x-axis line is y = 0

Answer 12

I would say 0 :)

Answer 13

here another example