Objective
By the end of this lesson, you will be able to understand how the domain of a linear function relates to its graph and the quantitative relationship it describes.
Materials and Prep
- Paper
- Pencil
- Ruler
- Calculator (optional)
No prior knowledge is required for this lesson.
Activities
- Graphing Linear Functions: Draw the graph of a simple linear function such as y = 2x + 3. Observe how changing the domain affects the graph.
- Domain Exploration: Choose different domains for the same linear function and observe how it impacts the graph. Discuss how the domain restricts the input values of the function.
- Real-life Examples: Create a scenario where a linear function represents a real-life situation. Discuss how the domain of the function relates to the context of the problem.
Talking Points
- Understanding Domain: "The domain of a function represents all possible input values for the function."
- Graphical Representation: "When we graph a linear function, the domain is represented on the x-axis, and the range is represented on the y-axis."
- Quantitative Relationship: "The domain of a linear function helps us understand the set of values for which the function is defined and meaningful."
- Real-world Application: "In real-life scenarios, the domain of a linear function can represent constraints or limitations based on the context of the problem."
- Exploring Different Domains: "By changing the domain of a linear function, we can see how the graph and the relationship it describes are affected."