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Build a Function Activity

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.

Build a Function Activity

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

Build a Function Activity

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

Build a Function Activity

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

Build a Function Activity

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

Build a Function Activity

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.

Build a Function Activity

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.

Build a Function Activity

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.

Build a Function Activity

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

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Domain Codomain Range Function Evaluation Challenge (PDF) (201 downloads)


Domain Codomain Range Function Evaluation Challenge (Editable Publisher File ZIP) (112 downloads)