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