Question

1. which relation is a function?

a {(-3, 3), (5, 5), (-3, 2), (5, 3)}
b image of a vertical line on a coordinate grid
c table with domain and range: 4→3, 5→4, 2→5, 4→6
d image of points on a coordinate grid

Explanation:

Step1: Recall the definition of a function

A relation is a function if each input (domain value) is paired with exactly one output (range value). This can be checked using the vertical line test for graphs, or by ensuring no repeated domain elements in ordered pairs or tables.

Step2: Analyze Option A

The set of ordered pairs is \(\{(-3, 3), (5, 5), (-3, 2), (5, 3)\}\). Here, the domain value \(-3\) is paired with \(3\) and \(2\), and \(5\) is paired with \(5\) and \(3\). So, repeated domain values with different range values, not a function.

Step3: Analyze Option B

The graph is a vertical line. A vertical line means there are multiple \(y\)-values for a single \(x\)-value (fails vertical line test), so not a function.

Step4: Analyze Option C

The table has domain values: \(4\), \(5\), \(2\), \(4\). The domain value \(4\) is paired with \(3\) and \(6\) (repeated domain with different range), so not a function.

Step5: Analyze Option D

Using the vertical line test on the graph, any vertical line will intersect the graph at most once. So each \(x\)-value (domain) has exactly one \(y\)-value (range), so it is a function.

Answer:

D (the graph in option D)