_____ / 24

No Calculator Allowed

For all questions on this test, let $f\left(x\right)=\frac{x^3-x^2-2x}{x^2-4}$.

First, the factorization: $\frac{\left(x\right)\left(x-2\right)\left(x+1\right)}{\left(x+2\right)\left(x-2\right)}$. The common factor of $\left(x-2\right)$ indicates a hole at $x=2$; its y-coordinate is at $\frac{\left(2\right)\left(2+1\right)}{\left(2+2\right)}=\frac{3}{2}$. For all other questions, the rational function is really $\frac{\left(x\right)\left(x+1\right)}{x+2}=\frac{x^2+x}{x+2}$.

It is at $x=-2$.

They are at $\left(0,0\right)$ and $\left(-1,0\right)$.

Division time!

$\begin{array}{rrrr}\hfill -2& \hfill 1& \hfill 1& \hfill 0\\ \hfill & \hfill & \hfill -2& \hfill 2\\ \hfill & \hfill 1& \hfill -1& \hfill 2\end{array}$

The end behavior asymptote is at $y=x-1$.

Page last updated 14:35 2021-03-16