SOLUTION: Consider the following function: f(x)=x+3/(x^2-5x-24) a. Determine the vertical asymptotes I got x=-3 and x=8 b. determine the location of any holes(give the ordered pair)

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Consider the following function: f(x)=x+3/(x^2-5x-24) a. Determine the vertical asymptotes I got x=-3 and x=8 b. determine the location of any holes(give the ordered pair)       Log On


   

Question 851247: Consider the following function: f(x)=x+3/(x^2-5x-24)
a. Determine the vertical asymptotes
I got x=-3 and x=8
b. determine the location of any holes(give the ordered pair)
c. determine the horizontal asymptote if it exists
y=0 is what I got
I already solved part A and C but I would like to double check my answers and I am not sure how to find the location of a hole for part B. If you could help me a would appreciate it. Thanks
Answer by josgarithmetic(39626) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=%28x%2B3%29%2F%28x%5E2-5x-24%29=%28x%2B3%29%2F%28%28x%2B3%29%28x-8%29%29

The factor of 1 as %28x%2B3%29%2F%28x%2B3%29 is undefined at x=-3, so that would be a hole in the graph. Division by zero is impossible.

The denominator will be undefined as will be the function when x=8; again because the denominator must not be zero, because division by zero is impossible. This will make x=8 a vertical asymptote.