anonymous
  • anonymous
What are the discontinuities of the function f(x) = x^2 + 5x + 6 ----------- 2x + 16
Mathematics
  • Stacey Warren - Expert brainly.com
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chestercat
  • chestercat
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anonymous
  • anonymous
This is torture.
anonymous
  • anonymous
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anonymous
  • anonymous
When the degree of the numerator is higher than the denominator, expect that you will have a slant asymptote. If the degree of numerator and denominator are the same, then you will have a horizontal asymptote. The zeros of the denominator will be your vertical asymptote. However, there is a special discontinuity that rational functions can have, which is called the "hole". To find these discontinuities, first simplify your rational function. Factor the numerator and the denominator, can you do this part for now?

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anonymous
  • anonymous
what is the factored form of \(\sf x^2 + 5x + 6\)?
anonymous
  • anonymous
I'm bad at simplifying but I know that the bottom is (x + 8)+(x + 8)
anonymous
  • anonymous
hmm let's try doing the easy way then. Do you know how to divide polynomials?
anonymous
  • anonymous
Kind of. I'm sorry, I hate math with a passion. Ask me anything about history or literature, but not math.
anonymous
  • anonymous
lol no worries. Since the numerator has a higher degree than the denominator, we will have a slant asymptote. To get the equation of the slant asymptote, divide the numerator by the denominator. Let's use long division:|dw:1447362040663:dw| can you try solving it? show me how you will do it.
anonymous
  • anonymous
the equation that you will get will be your slant asymptote. Next, let's find the vertical asymptote by finding the zeros of the denominator. 2x + 16, the common factor for these terms is 2. Now take out two, what will you end up with?

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