Question

explain: yes or no input -1 0 1 output -5 -1 0 3 yes or no are the rela

Explanation:

Step1: Recall function definition

A relation is a function if each input has exactly one output.

Step2: Analyze the input-output mapping

Input values: \(-1\), \(0\), \(1\).
Check each input:

• Input \(-1\): Let's see the arrows, it maps to some output (but we need to check if each input has only one output). Wait, looking at the diagram, does any input have multiple outputs? Wait, the input \(0\) – does it have more than one arrow? Wait, no, wait the input \(0\) – wait, no, let's re-examine. Wait, the input \(-1\), \(0\), \(1\): does any input have more than one output? Wait, looking at the arrows, maybe one of the inputs is mapped to multiple outputs? Wait, no, wait the problem is to check if it's a function. Wait, in a function, each input (x - value) has exactly one output (y - value). So let's list the mappings:

Input \(-1\): where does it map?
Input \(0\): how many outputs? If the arrow from \(0\) goes to more than one output, then it's not a function. Wait, from the diagram, the input \(0\) has an arrow to, say, maybe two outputs? Wait, the input \(0\) – looking at the red arrows, if \(0\) is connected to more than one output (like two different output values), then it's not a function. So let's check:

• Input \(-1\): let's see the arrow, maybe to \(-5\) or another? Wait, no, the key is: in a function, each input must have exactly one output. So if any input has two or more outputs, it's not a function.

Looking at the input \(0\): does it have more than one arrow (i.e., more than one output)? From the diagram, the input \(0\) seems to have arrows to multiple outputs (like two different output values). So that means the input \(0\) is mapped to more than one output. Therefore, the relation is not a function, so the answer is NO.

Answer:

NO (because the input \(0\) is mapped to more than one output, violating the definition of a function where each input must have exactly one output)