SOLUTION: what is the x intercept as an ordered pair and what is the vertical asymptotes as equations of vertical lines f(x)=(4x^3-64x)/(x^2+6)

Question 492058: what is the x intercept as an ordered pair and what is the vertical asymptotes as equations of vertical lines f(x)=(4x^3-64x)/(x^2+6)
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
what is the x intercept as an ordered pair and what is the vertical asymptotes as equations of vertical lines f(x)=(4x^3-64x)/(x^2+6)
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f(x)=(4x^3-64x)/(x^2+6)
To find the x-intercepts, set y=0, then solve for x by setting the numerator=0.
4x^3-64x=0
4x(x^2-16)
4x(x+4)(x-4)
x-intercepts: (-4,0), (0,0) and (4,0)
..
Vertical asymptotes
Normally, to find the vertical asymptotes, set the denominator=0, then solve for x. In given case, there is no vertical asymptote because the denominator can never be equal=0. You will get a non-real number when solving for x.
x^2+6=0
x^2=-6
x=�√-6
..
For your information, when vertical asymptotes are present, they are written as equations like x=1, x=3, x=5,... etc
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