SOLUTION: For the rational function f(x) = (x 2 - 1) / (x 2 - 9), give the intercepts and asymptotes and sketch the graph.

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Question 35982: For the rational function f(x) = (x 2 - 1) / (x 2 - 9), give the intercepts and asymptotes and sketch the graph.
Answer by stanbon(57399) About Me  (Show Source):
You can put this solution on YOUR website!
f(x) = (x^ 2 - 1) / (x^2 - 9), give the intercepts and asymptotes and sketch the graph.
x-intercept: let y=0 and solve for "x.
y will be zero if x^2-1 = 0;
y=0 if x=1 or x=-1
x-intercepts are (1,0) and (-1,0)
y-intercept: let x=0 and solve for "y".
y=(-1/-9)= 1/9
y-intercept at (0,1/9)
Horizontal asymptote:
Highest power of x is x^2/x^2. Horizontal asymptote is y=1
Vertical asymptote:
Denominator is zero when x=3 or x=-3. Vertical asymptotes at x=3 and x=-3.
With all this information you should be able to sketch the graph
Cheers,
stan H.