Question

the table of values are shown. what is the range of the relation? from least to greatest. the table has x and y columns with rows: (0, -4), (2, -8), (-3, 4). options: (-8,-4,4), (-3,2,6), (-4,-8,-3), (6,2,-3)

Explanation:

Step1: Recall range definition

Range of a relation is the set of all \( y \)-values (outputs) from the ordered pairs \((x,y)\).
From the table, the ordered pairs are \((6, -4)\), \((2, -8)\), \((-3, 4)\). So the \( y \)-values are \(-4\), \(-8\), \(4\)? Wait, no, wait the table: first row \( x=6 \), \( y=-4 \); second \( x=2 \), \( y=-8 \); third \( x=-3 \), \( y=4 \). Wait, but the options have \(-8, -4, 4\). Wait, let's list the \( y \)-values: \(-4\), \(-8\), \(4\). Now order them from least to greatest: \(-8\) (least), then \(-4\), then \(4\) (greatest). So the range is \((-8, -4, 4)\).

Step2: Check options

Option 1: \((-8, -4, 4)\) matches the ordered \( y \)-values from least to greatest. Other options have \( x \)-values (like \(-3, 2, 6\) are \( x \)-values) or incorrect \( y \)-values.

Answer:

\((-8, -4, 4)\) (the first option)