anonymous
  • anonymous
State the horizontal asymptote of the rational function. f(x) = x + 9 / x^2 + 8x + 8
Mathematics
  • Stacey Warren - Expert brainly.com
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schrodinger
  • schrodinger
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DebbieG
  • DebbieG
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?
anonymous
  • anonymous
Yes, so it is horizontal because the denominator is bigger than the numerator
anonymous
  • anonymous
One way of viewing it is to plug in a very large number x :) and evaluate

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DebbieG
  • DebbieG
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
anonymous
  • anonymous
(x + 9) / (x^2 + 8x + 8) just pick x= 999
DebbieG
  • DebbieG
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?
anonymous
  • anonymous
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
jdoe0001
  • jdoe0001
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
anonymous
  • anonymous
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
anonymous
  • anonymous
so y = x
jdoe0001
  • jdoe0001
well the x-axis line is y = 0
anonymous
  • anonymous
I would say 0 :)
anonymous
  • anonymous
here another example |dw:1377815631899:dw|
anonymous
  • anonymous
Ahh okayy ! Thanks everyone !!

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