Question

Which answer choice shows the range of this piecewise function in interval notation?

Answer 1

`(-\text{infinity, -1) }\cup\text{ }\lbrack2,\text{ infinity) (third option)}`Step-by-step explanation:

The range are the y values of a function.

We have two arrows on the graph

The arrow by the left:

The y value is between y = -1 towards the negative y axis

Since the circle at the end of te arrow is open, it means -1 is not included. This is represented as (

`\begin{gathered} \text{In interval notation}\colon \\ (-\text{infinity, -1)} \end{gathered}`

The arrow by the right:

The y value starts at y = 2 and extends to the positive side of the y axis

The circle at the end is shaded, this means y = 2 is included. This is represented as [

`\begin{gathered} In\text{ interval notation:} \\ \lbrack2,\text{ infinity)} \end{gathered}`

Combining both function as piece-wise function:

`\begin{gathered} \text{Range:} \\ (-\text{infinity, -1) }\cup\text{ }\lbrack2,\text{ infinity) (third option)} \end{gathered}`