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 \(\left\lbrace\left(-3,5\right),\left(0,2\right),\left(3,5\right)\right\rbrace\). 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: List the inputs and outputs separately. Inputs: \(\{-3, 0, 3\}\); Outputs: \(\{5, 2, 5\}\). Note that the output \$5$ appears twice, but this 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 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: Since no input is associated with more than one output, the relation satisfies the definition of a function.
5. Step 5: Summarize the conclusion: The inputs are \(\{-3, 0, 3\}\), the outputs are \(\{5, 2, 5\}\), and the relation is a function because each input maps to exactly one output.