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I created this short and sweet build a function activity to give my Algebra 2 students extra practice using some of our new vocabulary: domain, codomain, and range.

This activity was designed to accompany Section 1.2 (Introduction to Functions) of Shaun Carter’s Full Year of Algebra 2 Notes. I will be honest. Even though I was a math major in college, I don’t remember learning about the difference between codomain and range. So, this was a new concept for both myself and my students!

The set of all x-values in a relation is called the domain. The codomain contains all of the y-values. The range is the subset of the codomain that contains the values that are actually produced by the function.

For example, take the function f(x) = x^2. The domain is all real numbers. The codomain is also all real numbers. However, the range is only those real numbers which are greater than or equal to 0.

I began by typing up six statements to describe a function. These statements included the function’s domain, codomain, and range. Then, I showed what the function evaluated to at three separate points.

I hung these statement cards to the dry erase board at the front of my classroom with magnetic clips.

I challenged students to draw a function that met this criteria on their individual dry erase boards.

Most students chose to draw a mapping diagram. They started by filling in the domain and codomain.

Some students tried to draw a table. They ran into some issues since in this activity, the codomain and the range are not identical.

Next, most students proceeded by filling in the given information. f(0) = 5, so 0 maps to 5. f(-3) = 11, so -3 maps to 11. Finally, f(4) = 5, so 4 maps to 5. At this point most students fell into one of two categories.

Some students thought they were done at this point since they believed they had used all of the given information. Other students became frustrated and claimed that I had not given them enough information to be able to complete the problem.

After a class discussion, most students began to realize that we had yet to use the fact that the range was {5, 9, 11}. The three function evaluation facts that we were given only mapped values to 5 and 11. We still needed something to map to 9. 7 is in the codomain but not the range, so nothing will map to 7.

This was a great activity for kicking off class, getting our brains working, and reviewing our vocabulary from the previous day.

## Free Download of Build a Function Activity

Domain Codomain Range Function Evaluation Challenge (PDF) (1161 downloads )

Domain Codomain Range Function Evaluation Challenge (Editable Publisher File ZIP) (908 downloads )

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