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Video: Determining Whether a Relation Represented by an Arrow Diagram Is a Function

Bethani Gasparine

Determine whether the following statement is true or false: The given figure represents a function.

01:59

Video Transcript

Determine whether the following statement is true or false: The given figure represents a function.

A function is a relationship that assigns exactly one output value for each input value. Here in our figure, the 𝑥 represents the input values and 𝑦 represents the output values. So for this to be a function, there should be exactly one output value, exactly one 𝑦, for each input value, each 𝑥. So for this to be a function, it’s key that there’s only one output value for each input value. So let’s go through each input value, the 𝑥s, and make sure that there’s only one output value.

The input value of four goes with the output value seven. So there’s exactly one output value, seven, for the input value four.

The input value of five has two outputs. It has an output of two and nine. So that input value of five does not have exactly one output; it has two. That means this figure cannot represent a function. So our answer is: False.

Now the input value of eight does go with the output value of five, and it has exactly one output, five. However, the fact that the input value of five has two output values, two and nine, means the given figure does not represent a function. So the following statement, the given figure represents a function, is false.