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.
[tex]f(x) = 3[/tex] if [tex]x <2[/tex], [tex]f(x) = -3[/tex] if [tex]x> 2[/tex], [tex]f(x) = 1[/tex] if [tex]x = 2[/tex]
We must find the limit when x approaches 2 from the left
[tex]\lim_{x \to 2^-}f(x)[/tex]
and we must find the limit when x approaches 2 on the right.
[tex]\lim_{x \to 2^+}f(x)[/tex]
when x approaches 2 on the left then [tex]x <2[/tex]. If [tex]x <2[/tex] then [tex]f (x) = 3[/tex], therefore the [tex]\lim_{x \to 2^-}f(x)=3[/tex]
When x approaches 2 on the right then [tex]x> 2[/tex]. If [tex]x> 2[/tex] then [tex]f (x) = -3[/tex], therefore the [tex]\lim_{x \to 2^+}f(x)=-3[/tex].
