document.write( "Question 35982: For the rational function f(x) = (x 2 - 1) / (x 2 - 9), give the intercepts and asymptotes and sketch the graph. \n" ); document.write( "

Algebra.Com's Answer #22292 by stanbon(75887) $\"\"$ $\"About$

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f(x) = (x^ 2 - 1) / (x^2 - 9), give the intercepts and asymptotes and sketch the graph.
\n" ); document.write( "x-intercept: let y=0 and solve for \"x.
\n" ); document.write( "y will be zero if x^2-1 = 0;
\n" ); document.write( "y=0 if x=1 or x=-1
\n" ); document.write( "x-intercepts are (1,0) and (-1,0)
\n" ); document.write( "y-intercept: let x=0 and solve for \"y\".
\n" ); document.write( "y=(-1/-9)= 1/9
\n" ); document.write( "y-intercept at (0,1/9)
\n" ); document.write( "Horizontal asymptote:
\n" ); document.write( "Highest power of x is x^2/x^2. Horizontal asymptote is y=1
\n" ); document.write( "Vertical asymptote:
\n" ); document.write( "Denominator is zero when x=3 or x=-3. Vertical asymptotes at x=3 and x=-3.
\n" ); document.write( "With all this information you should be able to sketch the graph
\n" ); document.write( "Cheers,
\n" ); document.write( "stan H. \n" ); document.write( "

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