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)

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) (Show Source): You can put this solution on YOUR website!

The factor of 1 as 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.
RELATED QUESTIONS
Find the equations for the horizontal and vertical asymptotes of the following. Type... (answered by stanbon)

Consider the two functions: f(x)=x^2-4 and g(x)=2x^3-3x^2-5x+6 A. A function is defined... (answered by greenestamps)

Find the horizontal and vertical asymptotes of the following: A) f(x)= 2x+3/x+2 B)... (answered by Nate)

determine the vertical asymptotes of the function... (answered by jim_thompson5910)

Find the horizontal and vertical asymptotes of the following. Type none if the function... (answered by stanbon)

Find the equations of the horizontal and vertical asymptotes for the following. Tye none (answered by jim_thompson5910)

I would really like it if you help me in the following function notations questions. (answered by algebrahouse.com)

Please show work Consider the function f(x)=(x^2-1)/(x-3) a Find the domain for... (answered by Boreal)

Find the vertical asymptotes,if exist,of the following functions. a) f(x)=5x/(3x^2+4)... (answered by josgarithmetic)