SOLUTION: Please show me how to sketch the graph of the rational function y=4x/(x^3-4x).

Question 593558: Please show me how to sketch the graph of the rational function y=4x/(x^3-4x).
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Please show me how to sketch the graph of the rational function
y=4x/(x^3-4x)
y=4x/x(x^2-4)
y=4/(x^2-4)
y=4/(x+2)(x-2)
..
x-intercept: none (because numerator is a constant,y≠0)
y-intercept=-1 (set x=0)
horizontal asymptotes:x-axis or y=0 (degree of numerator less then degree of denominator)
Vertical asymptotes:
set denominator=0, then solve for x:
(x+2)(x-2)=0
x=-2
and
x=2
vertical asymptotes at x=2 and x=-2
number line:
<...+....-2....-.....2.....+....>
You now have the information you need to draw the graph of given function
see graph below:

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