Question

four relations are shown below. click on the tabs to see them.
relation 1 relation 2 relation 3 relation 4
domain range
diagram of mapping from domain elements to range elements
check the box corresponding to each relation that represents a function.
☐ relation 1 ☐ relation 2 ☐ relation 3 ☐ relation 4 ☐ none of the relations

Explanation:

To determine if a relation is a function, we use the vertical line test (or the definition: a relation is a function if each input in the domain has exactly one output in the range).

Analyzing Relation 1 (from the diagram):

• Domain elements: \( y, e, b, g \)
• Range elements: \( -5, 2 \)
• Check: Each domain element maps to only one range element (\( y \to -5 \), \( e \to -5 \), \( b \to 2 \), \( g \to 2 \)). No domain element has more than one output. Thus, Relation 1 is a function.

For Relations 2, 3, 4 (not shown, but assuming the problem’s context):

Since the diagram only shows Relation 1, and the other relations are not visible, we can only confirm Relation 1 (if the diagram is for Relation 1). However, based on the given diagram for Relation 1:

Answer:

\(\boldsymbol{\square}\) Relation 1 (check the box for Relation 1, as it satisfies the function definition).

(Note: If other relations were shown, we would analyze them similarly, but only Relation 1 is visible in the provided diagram.)