Use the graph of the rational function f(x) to fill in the blanks below

As X---- 2-, f(x)--- ___ ?

Question

Use the graph of the rational function f(x) to fill in the blanks below 

As X----> 2-, f(x)---> ___ ?

anonymous · Answer

attachment

aaronq · Answer

There is an asymptote when approaching from either side, so $\sf f(-2)=\pm\infty$.

anonymous · Answer

what about for -inf, inf, and 2?

anonymous · Answer

it wont let me use a list of numbers as an answer. Entering -inf,inf is wrong

aaronq · Answer

"2-" can mean "negative two", or "approaching 2 from the left side".  If it's approaching 2 (or in this case -2 also) from the left side then it's $+\infty$.

aaronq · Answer

for $x\rightarrow \pm \infty$, look at the asymptote of the graph, f(x)=-3 for both scenarios

anonymous · Answer

Okay so +2 is -inf. But yeah I'm stuck on the + and - infinities

aaronq · Answer

Look at the y-axis where the horizontal asymptote line is. What value is the dotted line on?

anonymous · Answer

-3

anonymous · Answer

so is it -3 for both the - and + infinities?

aaronq · Answer

yes

anonymous · Answer

thank you!!

aaronq · Answer

no problem !