How do you identify all asymptotes or holes and intercepts for #f(x)=(x+3)/(x^2+7x+12)#?
First you need to factor the denominator.
Now you will have
Now cancel out any like terms, in this case the
to find your y component, plug in
This equals to
so the coordinate for your hole would be
Now you still have the
- note that when two like values cancel out there is a whole and when there are no values cancelling out then the zero of
#x#in the denominator will be your V.A. *
Now we can check for horizontal asymptotes. H.A.s exist only when the numerator's leading degree is less than or equal to the leading degree of the denominator.
In this case the degree of the numerator is x and the degree of the denominator is
Finally we can check for Slant asymptotes. S.A.s exist where the degree of the numerator is 1 greater than the degree of the denominator. In this case the numerator has a degree smaller than the denominator. This means we will not have a slant asymptote.
We look at the zeros of the numerator however we already cancelled out the zero
To find the y intercept plug in 0 for x in the remaining equation which is
S.A: does not exist
X int: does not exist