Question

polynomial end behavior question

Answer 1

i think

Answer 2

the original question was to determine if it has a slant asymptote so i did long division, but I felt like there wasnt one so i graphed it and i didnt see any spot for the slant asymptote to go.

Answer 3

\[\large \dfrac{-x^3 -2x^2 + x + 1}{x^2 + 1} = \color{red}{-x-2} + \dfrac{2x+3}{x^2+1} \]

Answer 4

ok so the leading term is just -x

Answer 5

the slant asymptote would be \(\large \color{red}{y = -x-2}\)

Answer 6

so the slant asmyptote can cut through the center of the graph?

Answer 7

x->oo f(x)->-oo
x->-oo f(x)->oo

Answer 8

that looks good to me !

Answer 9

i think so, it can cut the graph at other parts..