document.write( "Question 559324: how do i graph this radical function.... y=4x/x^3-4x? \n" ); document.write( "

Algebra.Com's Answer #363466 by lwsshak3(11628) $\"\"$ $\"About$

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how do i graph this rational function.... y=4x/x^3-4x?
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\n" ); document.write( "y=4x/x^3-4xd
\n" ); document.write( "y=4x/x(x^2-4)
\n" ); document.write( "y=4/(x+2)(x-2)
\n" ); document.write( "..
\n" ); document.write( "When degree of denominator less than degree of numerator,
\n" ); document.write( "horizontal asymptote=x-axis.
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\n" ); document.write( "Vertical asymptotes, set denominator=0, then solve for x:
\n" ); document.write( "(x+2)(x-2)=0
\n" ); document.write( "Vertical asymptotes: -2 & 2
\n" ); document.write( "..
\n" ); document.write( "Y-intercept: set x=0,
\n" ); document.write( "y-intercept=4/-4=-1
\n" ); document.write( "..
\n" ); document.write( "x-intercepts: normally, we set y=0, then solve for x, but y cannot be zero because numerator is a constant=4
\n" ); document.write( "x-intercept: none
\n" ); document.write( "..
\n" ); document.write( "number line:
\n" ); document.write( "<...+...-2....-....2...+....>
\n" ); document.write( "When x>2, function>0. Moving left on line, intervals switch signs when going thru zeros of multiplicity 1
\n" ); document.write( "..
\n" ); document.write( "You now have all the information you need to graph given rational function.
\n" ); document.write( "It should look much like the graph below:
\n" ); document.write( " $\"+graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C4%2F%28x%2B2%29%28x-2%29%29+\"$ \n" ); document.write( "

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