Question

I need this answered please

Answer 1

Answer:

Second Option: 3, -3

Step-by-step explanation:

In the graph of the supplied function we observe f (x) is a piece wise function composed of two line segments and a point.

$f(x) = 3$   if   $x$, $f(x) = -3$   if  $x> 2$, $f(x) = 1$ if $x = 2$

We must find the limit when x approaches 2 from the left

$\lim_{x \to 2^-}f(x)$

and we must find the limit when x approaches 2 on the right.

$\lim_{x \to 2^+}f(x)$

when x approaches 2 on the left then $x$. If $x$ then $f (x) = 3$, therefore the $\lim_{x \to 2^-}f(x)=3$

When x approaches 2 on the right then $x> 2$. If $x> 2$ then $f (x) = -3$, therefore the $\lim_{x \to 2^+}f(x)=-3$.