# How do you identify all asymptotes or holes and intercepts for #f(x)=(x^3-4x)/(x^2-x)#?

##### 1 Answer

V.A.

H.A. non

S.A.

HOLE.

#### Explanation:

. 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

S.A. :

.There is a hole at (0,4)

factor x from numerator and denominator

rewrite 4 as

factor

the common factor is x