How do you identify all asymptotes or holes and intercepts for #f(x)=(x^3-4x)/(x^2-x)#?
. For a function to have V.A. the function needs to have undefined points (zeros of denominator)
In this function, the zeros of the denominator are 0 and 1 therefore the vertical asymptotes are
. A graph will have a horizontal asymptote if the degree of the denominator is greater than the degree of the numerator
In this function, the degree of nominator is 3 and the degree of numerator is 2
. Since the degree is one greater in the numerator, I know that I will have a slant asymptote.
Use polynomial long division to get the Slant/Oblique asymptote
.There is a hole at (0,4)
factor x from numerator and denominator
rewrite 4 as
the common factor is x