Question

what is the range of this function?
graph of a coordinate plane with several purple points plotted at (-4, -1), (-3, 3), (-2, 2), (1, 5), (3, 3), (5, 2)
options:
{ -4, -2, 1, 3, 5 }
{ -1, 2, 5 }
{ -1, 2, 3, 5 }
{ -4, -3, -2, 1, 3, 5 }

Explanation:

Step1: Recall the definition of range

The range of a function is the set of all possible \( y \)-values (outputs) of the function. So we need to identify the \( y \)-coordinates of all the plotted points.

Step2: Identify the \( y \)-coordinates of the points

Looking at the graph, the points (from left to right) have coordinates:

• \( (-4, -1) \): \( y \)-value is \( -1 \)
• \( (-3, 3) \): \( y \)-value is \( 3 \)
• \( (-2, 2) \): \( y \)-value is \( 2 \)
• \( (1, 5) \): \( y \)-value is \( 5 \)
• \( (3, 3) \): \( y \)-value is \( 3 \) (but we already have 3, so we don't repeat)
• \( (5, 2) \): \( y \)-value is \( 2 \) (already have 2)

So the distinct \( y \)-values are \( -1, 2, 3, 5 \).

Answer:

\(\{-1, 2, 3, 5\}\)