Question

determine which relation is also a function.

Explanation:

Step1: Recall Function Definition

A function is a relation where each input (x - value) has exactly one output (f(x) - value). So we check each relation for repeated x - inputs with different outputs.

Step2: Analyze Top - Left Relation

In the top - left relation, check x - values:

• x = - 4: maps to - 7
• x = - 2: maps to 2
• x = 0: maps to 4
• x = 2: maps to 6
• x = 4: maps to 9

Wait, no, looking again, x = 0 seems to map to 4 and maybe another? Wait, no, let's re - check. Wait, the top - left: x=-4→-7; x = - 2→2; x = 0→4; x = 2→6; x = 4→9? Wait, no, maybe I misread. Wait, the top - left: x=-4 has an arrow to - 7, x=-2 to 2, x = 0 to 4, x = 2 to 6, x = 4 to 9? No, maybe the arrows are different. Wait, no, the bottom - right relation:
x=-2→-6; x=-1→-3; x = 0→0; x = 1→2; x = 2→5. Each x has exactly one arrow.

Wait, let's check each:

1. Top - Left: Check x - values. Does any x have more than one arrow? Let's see, x = 0: how many arrows? If x = 0 has more than one arrow, it's not a function. From the diagram, x = 0 in top - left has two arrows? So not a function.

1. Top - Right: x=-1 has two arrows (to 1 and - 3? Wait, no, the top - right: x=-1 has arrows to 1 and - 3? Wait, x=-2 has an arrow to - 3, x=-1 has arrows to 1 and - 3? So x=-1 has two outputs, not a function.

1. Bottom - Left: x = 2 has how many arrows? If x = 2 has more than one arrow, not a function. From the diagram, x = 2 has multiple arrows, so not a function.

1. Bottom - Right: x=-2→-6; x=-1→-3; x = 0→0; x = 1→2; x = 2→5. Each x has exactly one output. So this relation is a function.

Answer:

The bottom - right relation (where x = - 2 maps to - 6, x=-1 maps to - 3, x = 0 maps to 0, x = 1 maps to 2, x = 2 maps to 5) is the function.