Question

determine whether the relation defines a function, and give the domain and range.

does the relation define a function?
a. no, because every vertical line intersects the graph of a relation in no more than one point.
b. no, because at least one vertical line intersects the graph of a relation in no more than one point.
c. yes, because at least one vertical line intersects the graph of a relation in no more than one point.
d. yes, because every vertical line intersects the graph of a relation in no more than one point.

Explanation:

Step1: Apply Vertical Line Test

A relation is a function if every vertical line intersects its graph at most once. The given graph is a straight line (non-vertical), so any vertical line will cross it at exactly one point.

Step2: Evaluate Options

Match the test result to the correct option. The valid reasoning for a function is that every vertical line intersects the graph in no more than one point.

Answer:

D. Yes, because every vertical line intersects the graph of a relation in no more than one point.

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Domain and Range (from the graph):

The line extends infinitely in both directions, so:

• Domain: All real numbers, written as $(-\infty, \infty)$
• Range: All real numbers, written as $(-\infty, \infty)$