Question

1. which relation is a function?

a {(-3, 3), (5, 5), (-3, 2), (5, 3)}
b graph of a vertical line
c

domain	range
4	3
5	4
2	5
4	6

d graph with plotted points

Explanation:

Step1: Recall the definition of a function

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

Step2: Analyze Option A

The set 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 (since it's a straight line parallel to the \(y\)-axis). By the vertical line test, a vertical line intersects the graph at infinitely many points, meaning one \(x\)-value (input) has multiple \(y\)-values (outputs). 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 \(6\). So, repeated domain value with different range values. Not a function.

Step5: Analyze Option D

For the graph, we apply the vertical line test. Any vertical line drawn will intersect the graph at most once. This means each \(x\)-value (input) has exactly one \(y\)-value (output). So, it is a function.

Answer:

D (the graph in option D)