document.write( "Question 593558: Please show me how to sketch the graph of the rational function y=4x/(x^3-4x). \n" ); document.write( "

Algebra.Com's Answer #376557 by lwsshak3(11628) $\"\"$ $\"About$

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Please show me how to sketch the graph of the rational function
\n" ); document.write( "y=4x/(x^3-4x)
\n" ); document.write( "y=4x/x(x^2-4)
\n" ); document.write( "y=4/(x^2-4)
\n" ); document.write( "y=4/(x+2)(x-2)
\n" ); document.write( "..
\n" ); document.write( "x-intercept: none (because numerator is a constant,y≠0)
\n" ); document.write( "y-intercept=-1 (set x=0)
\n" ); document.write( "horizontal asymptotes:x-axis or y=0 (degree of numerator less then degree of denominator)
\n" ); document.write( "Vertical asymptotes:
\n" ); document.write( "set denominator=0, then solve for x:
\n" ); document.write( "(x+2)(x-2)=0
\n" ); document.write( "x=-2
\n" ); document.write( "and
\n" ); document.write( "x=2
\n" ); document.write( "vertical asymptotes at x=2 and x=-2
\n" ); document.write( "number line:
\n" ); document.write( "<...+....-2....-.....2.....+....>
\n" ); document.write( "You now have the information you need to draw the graph of given function\r
\n" ); document.write( "\n" ); document.write( "see graph below:
\n" ); document.write( " $\"+graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C4x%2F%28x%5E3-4x%29%29+\"$ \n" ); document.write( "

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