Question

What are the discontinuities of the function
f(x) = x^2 + 5x + 6
-----------
2x + 16

Answer 1

This is torture.

Answer 2

@VXVIVX @Vocaloid @zepdrix @Data_LG2 @dan815 @pooja195 @Preetha

Answer 3

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?

Answer 4

what is the factored form of \(\sf x^2 + 5x + 6\)?

Answer 5

I'm bad at simplifying but I know that the bottom is (x + 8)+(x + 8)

Answer 6

hmm let's try doing the easy way then. Do you know how to divide polynomials?

Answer 7

Kind of.

I'm sorry, I hate math with a passion. Ask me anything about history or literature, but not math.

Answer 8

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:

can you try solving it? show me how you will do it.