Question

Given the following rational function:

(a) state the domain.

(b) find the vertical and horizontal asymptotes, if any.

(c) find the oblique asymptotes, if any.

(d) submit a graph.

Please show all of your work.
f(x)=x^2+6x-8/x-5

Answer 1

are you allowed to use a computer?

Answer 2

ha ha yes- I just dont know how to input this to find the answers

Answer 3

OK, well, wolfram alpha is great for graphs -- http://www.wolframalpha.com/input/?i=%28x%5E2%2B6x-8%29%2F%28x-5%29

Answer 4

as you can see there's a region in the center where the line goes off the chart. in this area the function is not defined.

If you look at the way Wolfram Alpha draws your equation you can see x-5 is in the denominator. This means the domain does not include 5 - because if x=5, then the denominator is 0 and dividing by 0 is not defined.

Answer 5

a vertical asymptote is a line that the function gets closer and closer to but never reaches -- again, x=5

Answer 6

hmm