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Linear Functions and Graphing
After determining whether a given equation is linear or non-linear, the next step is to investigate what it means for an equation, relation, or graph to represent a function. From here, we can then use function notation to describe a linear equation and graph linear functions on the coordinate plane.
In this subtopic we will define a relation and then use the component of a relation, domain and range, to help us define a function. The vertical line test will be explored along with function notation. Student will then use the concepts introduced to graph linear functions using ordered pairs and x- and y-intercepts.
Important definitions include those for:
• relation
• domain
• range
• function
• vertical line test
• function notation
• linear function
In this subtopic, we begin with lecture notes for use by the instructor with students or as an individual student activity. In the lecture notes, we define important terms, determine whether a relation is a function from a set, an equation, or graph, evaluate functions, and graph linear functions using ordered pairs and x- and y-intercepts. Elements within the lecture notes may be used to assess understanding of the content.
Activity two, I Have. . .Who Has? Activity, is designed to use in the classroom and encourages students to become involved in the learning process. At the conclusion of the activity, students should be proficient in determining the characteristics of a graph or equation, recognize a graph from an equation or function, and compare how a function, equation, and graph relate to each other.
Activity three, Get the Picture Activity, can be used as a take-home assignment for students or as an in-class group activity. At the conclusion of the activity, students should be able to graph a linear equation and use the domain given to bound each equation.
In the summary, instructors are provided with a Pre-Test and Post-Test of the subtopic. Instructors may choose to use both tests, or only the Post-Test as a final assessment.