Video Transcript
Which of the following relations represents a function?
In this question, we’re given two mapping diagrams labeled relation A and relation B. We recall that a relation or mapping transforms elements from the input set onto elements of the output set. If every input in a mapping has exactly one output, it is called a function. Functions can be either one to one, where one input has one output, or many to one, where many inputs map on to the same output.
When we consider relation A, we see that every input has a single output. The input of negative three maps onto the output of positive three. Negative two maps on to negative six, negative one maps on to zero, zero maps on to 15, and one maps on to negative one. Therefore, relation A represents a function.
When we consider relation B, we observe that the input of one maps on to two different outputs, zero and 15. For a relation to be a function, we will need to see that each input maps on to no more than one output. Therefore, relation B does not represent a function because the input of one maps onto more than one output.
In conclusion, our answer is relation A because it represents a function. In fact, this is a one-to-one function where one input maps onto each output.
