SOLUTION: Describe the vertical asymptote(s) and hole(s) for the graph of y = (x - 3)(x - 1)/(x - 1)(x - 5) A. asymptote: x = 5 and hole: x = 1 B. asymptote: x = –5 and hole: x

Algebra ->  Rational-functions -> SOLUTION: Describe the vertical asymptote(s) and hole(s) for the graph of y = (x - 3)(x - 1)/(x - 1)(x - 5) A. asymptote: x = 5 and hole: x = 1 B. asymptote: x = –5 and hole: x       Log On


   

Question 625809: Describe the vertical asymptote(s) and hole(s) for the graph of
y = (x - 3)(x - 1)/(x - 1)(x - 5)
A. asymptote: x = 5 and hole: x = 1

B. asymptote: x = –5 and hole: x = –1

C. asymptote: x = –3 and hole: x = 5

D. asymptote: x = 5 and hole: x = –1

Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Describe the vertical asymptote(s) and hole(s) for the graph of
y+=+%28x+-+3%29%28x+-+1%29%2F%28x+-+1%29%28x+-+5%29
(x-1) cancels out, leaving the graph of +%28x-3%29%2F%28x-5%29
The asymptote for this graph is x=5, at which point the curve is undefined.
Also a hole occurs at x=1 which means x=1 is not in the domain of y.
So you have an asymptote at x=5 and a hole at x=1
see graph below as a visual check:
+graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C+%28x-3%29%2F%28x-5%29%29+