Previously, students reasoned about the domain and range of a function based on descriptions about the situation it represents, or from a rule that defines the function. In this lesson, students use graphs to learn about the domain and range of functions, while continuing to think about what values are reasonable in the given situations.
Students learn to look for graphical features that would help them identify restrictions to the input or output. For example, they recognize that maximums and minimums, intercepts, and gaps on the graph can be quite informative. They also see that discrete points or breaks in a graph suggest that not all values can be in the domain or range, and that a graph may only partially represent a function. The work here offers opportunities to look for and make use of structure (MP7).
As they examine graphs against situations and vice versa, students practice making sense of quantities (MP1) and reasoning concretely and abstractly (MP2). When describing domain and range, students also practice attending to precision by minding relevant details in the graphs and descriptions of functions (MP6).
In upcoming lessons, students will learn about piecewise functions and absolute value functions. The work here prepares them to make sense of the quantities in those functions, where the dependent variable behaves differently for different parts of the domain.
Advanced preparation, which includes data collection and organization, is needed for an upcoming lesson on absolute value functions. See Required Preparation for Absolute Value Functions (Part 1).
- Given a description of a function that represents a situation, determine reasonable domain and range.
- Practice interpreting key features of graphs in terms of the quantities represented.
Let’s analyze graphs of functions to learn about their domain and range.
- 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.