Question

what is the range of this relation? the image shows a coordinate grid with several purple points. the options are: {-4, -3, 1, 2, 5}, {-3, -2, -1, 2}, {-3, -1, 2, 5}, {-4, -2, 1, 2}

Explanation:

Step1: Identify the y - coordinates of the points

First, we find the coordinates of each purple point from the graph:

• The point at \(x = - 4\) has \(y=-1\)
• The point at \(x=-2\) has \(y = 5\)
• The point at \(x = 1\) has \(y=2\) and \(y=-3\)
• The point at \(x = 2\) has \(y = 5\) and \(y=-1\)

Step2: List the unique y - values (range)

The range of a relation is the set of all output values (y - values) of the relation. So we collect all the unique \(y\) - coordinates: \(-3,-1,2,5\)

Answer:

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