Question

this is a mapping diagram and table of the input/output information. is this a function? inputs outputs 0 0 1 1 1 -1 2 4 2 -4

Explanation:

Step1: Recall the definition of a function

A function is a relation where each input (or domain element) has exactly one output (or range element). In other words, for every input value, there should be only one corresponding output value.

Step2: Analyze the given input - output pairs

• For the input \( 0 \), the output is \( 0 \) (only one output, so this is fine).
• For the input \( 1 \), we have two outputs: \( 1 \) and \( - 1 \) (from the table: when input is \( 1 \), outputs are \( 1 \) and \( - 1 \); also from the mapping diagram, \( 1 \) maps to both \( - 1 \) and \( 1 \)).
• For the input \( 2 \), we have two outputs: \( 4 \) and \( - 4 \) (from the table: when input is \( 2 \), outputs are \( 4 \) and \( - 4 \); also from the mapping diagram, \( 2 \) maps to both \( 4 \) and \( - 4 \)).

Since the inputs \( 1 \) and \( 2 \) have more than one output, the relation does not satisfy the definition of a function.

Answer:

No (the box next to "No" should be checked)