Problem

Asha found that a vertical line intersects the graph of $x=|y|$ at two points. What can Asha conclude about $x=|y|$ ? It is a function of $x$ but not a relation. It is a relation but not a function of $x$. It is both a function of $x$ and a relation. It is neither a function of $x$ nor a relation.

Solution

Step 1 :Asha found that a vertical line intersects the graph of \(x=|y|\) at two points.

Step 2 :The graph of \(x=|y|\) is a V-shaped graph that opens to the right.

Step 3 :A vertical line intersects the graph at two points, which means that for a single value of \(x\), there are two corresponding values of \(y\).

Step 4 :This violates the definition of a function, which states that for each input, there should be exactly one output.

Step 5 :However, it does satisfy the definition of a relation, which simply states that there is a relationship between the two variables.

Step 6 :\(\boxed{x=|y|}\) is a relation but not a function of \(x\).

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Source: https://solvelyapp.com/problems/7257/

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