Questions: Decide whether the relation is a function. x -1 2 6 9 10 y 8 -4 1 8 9 Select one: a. Not a function b. Function

Transcript text: Decide whether the relation is a function. \begin{tabular}{r|r|r|r|r|r} x & -1 & 2 & 6 & 9 & 10 \\ \hline$y$ & 8 & -4 & 1 & 8 & 9 \end{tabular} Select one: a. Not a function b. Function

Solution

Solution Steps

To determine if a relation is a function, we need to check if each input $ x $ maps to exactly one output $ y $. In other words, no $ x $ value should be associated with more than one $ y $ value.

Step 1: Identify the Relation

We are given the relation in tabular form: \[ \begin{array}{r|r|r|r|r|r} x & -1 & 2 & 6 & 9 & 10 \\ \hline y & 8 & -4 & 1 & 8 & 9 \end{array} \]

Step 2: Map $ x $ to $ y $

We map each $ x $ value to its corresponding $ y $ value: \[ \{-1: 8, 2: -4, 6: 1, 9: 8, 10: 9\} \]

Step 3: Check for Function Criteria

A relation is a function if each $ x $ value maps to exactly one $ y $ value. We check if the number of unique $ x $ values is equal to the number of unique pairs in the relation.

Step 4: Verify the Function

Since each $ x $ value in the given relation maps to exactly one $ y $ value, the relation satisfies the criteria for being a function.