State the inputs and outputs of the following relation. Is it a function?
$\{(-3,5),(0,2),(3,5)\}$

• A.
• B.
• C.
• D.

Answer: (C)

Verified step by step guidance

1. Step 1: Identify the inputs and outputs from the given relation. The relation is given as the set of ordered pairs \(\left\lbrace (-3,5), (0,2), (3,5) \right\rbrace\). Here, the inputs (or domain) are the first elements of each pair: \(-3\), \(0\), and \(3\). The outputs (or range) are the second elements of each pair: \(5\), \(2\), and \(5\).
2. Step 2: Write down the input set and output set separately. Inputs: \(\{ -3, 0, 3 \}\) and Outputs: \(\{ 5, 2 \}\). Notice that the output \(5\) appears twice, but that is allowed in a function as long as each input corresponds to exactly one output.
3. Step 3: Determine if the relation is a function. A relation is a function if every input has exactly one output. Check if any input value is paired with more than one output. Here, each input \(-3\), \(0\), and \(3\) has only one output (\(5\), \(2\), and \(5\) respectively).
4. Step 4: Conclude that the relation is a function because no input is associated with more than one output. Even though the output \(5\) repeats, it is paired with different inputs, which is allowed.
5. Step 5: Summarize: Inputs are \(\{ -3, 0, 3 \}\), outputs are \(\{ 5, 2 \}\), and the relation is a function.