SOLUTION: Good evening, I'm trying to find the y-intercept of the following: {{{y=(x^2-49)/(x-7)}}} I found the vertical asymptote of 7 and there is no horizontal asymptote. I calcu

Algebra ->  Equations -> SOLUTION: Good evening, I'm trying to find the y-intercept of the following: {{{y=(x^2-49)/(x-7)}}} I found the vertical asymptote of 7 and there is no horizontal asymptote. I calcu      Log On


   

Question 369304: Good evening, I'm trying to find the y-intercept of the following:
y=%28x%5E2-49%29%2F%28x-7%29
I found the vertical asymptote of 7 and there is no horizontal asymptote.
I calculated a y-intercept of 7 and I don't believe this is true based on the graph. Could you please help me find this?
Thanks!
Found 3 solutions by robertb, Alan3354, mananth:
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
The domain of the function is the set of all real numbers except x = 7. (Why?) Operating only within the domain enables us to make an important cancellation: y+=+%28%28x-7%29%28x%2B7%29%29%2F%28x-7%29+=+x+%2B7, x not equal to 7. The graph of this function is a straight line WITH A HOLE at the point (7,14), and y-intercept at 7. (So there is NO vertical asymtote!)

Answer by Alan3354(69443) About Me  (Show Source):
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
y=%28x%5E2-49%29%2F%28x-7%29
y+=+%28%28x%2B7%29%28x-7%29%29%2F%28x-7%29
..
(x-7) cancel off
y = x+7
this is a straight line graph
with intercepts (7,0)(0,-7)
graph%28300%2C300%2C-8%2C2%2C-2%2C8%2C%28%28x%5E2-49%29%2F%28x-7%29%29%29
there is no asymptote
..
m.ananth@hotmail.ca