Before this lesson, students have considered (even if only peripherally) input and output values that would make sense in the context of a function. Some examples:
- When analyzing the cost of buying bagels, it was intuitive to consider only positive whole numbers for the input.
- When studying the total number of barks of a dog as a function of time, it was natural to consider only positive whole numbers for the output.
- When looking at the height of a projectile as a function of time, it made sense to limit the input from the launch of the object to the moment the object hits the ground.
In this lesson and the next one, students focus their attention on possible input and output values, framing them as the domain and range of a function. In this lesson, they identify the domain and range of functions and describe them using words, lists of numbers, or inequalities (if appropriate). In the next lesson, students will relate the domain and range of a function with features of its graph.
Students' analyses of inputs and outputs continue to be grounded in context, allowing many chances to reason quantitatively and abstractly (MP2). In an optional activity, there is an opportunity to study the domain of a function without a context.
The insights students gain here will help them later in the unit and throughout the course, as they make sense of other kinds of functions—piecewise-defined, exponential, and quadratic. These understandings will also expand students' capacity to model with mathematics.
- Given a description of a function that represents a situation, determine reasonable domain and range.
- Understand that the domain of a function is the set of all possible inputs and the range is the set of all possible outputs.
Let’s find all possible inputs and outputs for a function.
Graphing technology is required for the optional activity What Could Be the Trouble? Acquire devices that can run Desmos (recommended) or other graphing technology. It is ideal if each student has their own device. (Desmos is available under Math Tools.)
- I know what is meant by the “domain” and “range” of a function.
- When given a description of a function in a situation, I can determine reasonable domain and range for the function.
The domain of a function is the set of all of its possible input values.
The range of a function is the set of all of its possible output values.