Lesson 4: Practical Domain and Range

What constitutes the domain of a function and what constitutes the range of a function?

Domain: Range

1. HSF-IF.A.1
Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of
the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x.

Lesson Description: In this lesson, students analyze the contextual constraints of functions. The "Practical Domain" and "Practical Range" are determined by the physical limitations of the scenario being modeled. Key topics include: Identifying Constraints: Recognizing that variables like time, distance, and number of people cannot be negative. Determining Endpoints: Finding the "starting value" (often the y-intercept) and the "ending value" (the point where the process stops, such as when an object hits the ground or a bank account reaches zero).Discrete vs. Continuous Contexts: Deciding if a domain should include all real numbers (like time or weight) or only whole numbers (like people or cars).Modeling Scenarios: Writing domain and range sets for real-world word problems using inequality notation and interval notation.
Purpose: The purpose of Section 7.4 is to develop logical modeling skills. It bridges the gap between pure mathematics and "common sense." By identifying the practical domain and range, students learn to filter out mathematically valid but physically impossible answers. This skill is critical for any field involving data analysis or budgeting, as it ensures that the mathematical models created are actually useful for making real-world predictions.
Depth of Knowledge (DOK) Level
DOK Level 3
Level 3 (Strategic Thinking & Complex Reasoning): This section is primarily DOK 3 because it requires students to move beyond the provided equation and use their own knowledge of the world to set boundaries. They must justify why certain values are excluded (e.g., "The domain ends at x=5 because that is when the water tank is empty") and synthesize the relationship between the independent and dependent variables to find the "peak" or "floor" of the range.

The distance a car travels from when the brakes are applied to the car's complete stop is the stopping distance. This includes time for the driver to react. The faster a car is traveling the longer the stopping distance. The stopping distance is a function of the speed of the car.

Function notation is sometimes difficult for student to comprehend. Stress that f(x) does not mean "f times x."
Students often confuse the domain and range. Stress the x is before y and d is before r.

Class and online work

Use practice problems 5-12, page 168-170 to assess students' understanding of the lesson concepts