Question

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

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

Answer 1

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

Answer 2

what about for -inf, inf, and 2?

Answer 3

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

Answer 4

"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 \(+\infty\).

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

-3

Answer 9

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

Answer 10

yes

Answer 11

thank you!!

Answer 12

no problem !