Question

I need this answered please

Answer 1

Second Option: 3, -3

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 <2`,
`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 <2`. If
`x <2` 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`.