004 Sample Final A, Problem 9

Graph the function. Give equations of any asymptotes, and list any intercepts.     $y={\frac {6}{x^{2}-x-2}}$

Foundations
What are the vertical asymptotes of $f(x)$?
Answer:
The vertical asymptotes are $x=a$ where $f(a)$ is undefined.

Solution:

Step 1:
Since $y={\frac {6}{(x-2)(x+1)}}$, the vertical asymptotes are $x=2$ and $x=-1$.

Step 2:
The horizontal asymptote is $y=0$.

Step 3:
There is no $x$ intercept since $y\neq 0$ for any $x$.
Plugging in $x=0$, we get $y=-3$. So, the $y$ intercept is (0,3)

Final Answer:
The vertical asymptotes are $x=2$ and $x=-1$. The horizontal asymptote is $y=0$. There is no $x$ intercept and the $y$ intercept is (0,3).

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