Samuel has been reviewing his notes on functions in preparation for the next test. He thinks it’s possible in a function for the amount of domain values to be greater than the amount of range values. Is Samuel correct? Explain why or why not.

He is incorrect.

Step-by-step explanation:

The range values cannot be greater than the domain values because of the known mathematical fact that all inputs (domain) can only have one output (range). This mathematical fact proves that the range can only be equal to the amount of inputs, not greater. To show why let's look at an example.

Ex:

Inputs:     Outputs:

   1                   2

   3                  2

   6                  2

Using that example we can already conclude that the domain values can be greater than the range values because each of the different inputs can have the same outputs as shown in the table above. But the thing with range is you can't have more than one output for the inputs. For example 1 (input) = 2 output and this will always equal 2 no matter what. You cannot have the inputs of 1 and have different outputs 2 and 4. Since you cannot have more than one output for an input it makes the amount of range values impossible to be greater than the domain values.

Hope that helped.