Find the slant asymptote and the vertical asymptotes of the given function. (If an answer does not exist, enter DNE.)
r(x) = x^3 + 9/2x^2 + x − 1
slant asymptote (write your entire equation, use y = )

Question

Find the slant asymptote and the vertical asymptotes of the given function. (If an answer does not exist, enter DNE.)
r(x) = x^3 + 9/2x^2 + x − 1
slant asymptote (write your entire equation, use y = )

campbell_st · Answer

the vertical asymptote occurs where 

$$2x^2 + x - 1 = 0$$

so you need to factorise to find the values for the x that make the denominator zero. 

the slant asymptote is found be polynomial division 

|dw:1361654868241:dw|


the quotient will be the slant asymptote, don't worry about the remainder/