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Linear Relationships and Functions

This chapter covers the fundamentals of linear relationships and functions, including simplified expressions using the distributive property and combining like terms. Students will learn to graph solutions on a number line, solve equations and inequalities in one variable—including absolute value equations. The chapter progresses to solving and graphing functions involving two variables on a coordinate plane and introduces concepts such as determining if a relation is a function using the vertical line test and functional notation.

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Linear Relationships and Functions

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  1. Chapter 2 Linear Relationships and Functions

  2. Where You’ve Been • Simplified expressions by using the Distributive Property and combining like terms. • Graphed solutions on a number line. • Solved equations and inequalities involving one variable. • Solved absolute value equations and inequalities involving one variable.

  3. Where You’re Headed • Solving equations (functions) and inequalities involving two variables. • Graphing solutions on a coordinate plane. • Solving absolute value equations involving two variables.

  4. Lesson 2-1 Relations and Functions

  5. Objectives • Graphing Relations • Identifying Functions

  6. A Relation is • Defined as a set of ordered pairs. • Each ordered pair has an input (x) and an output (y). • Ex.

  7. A Function is • A relation where each value of the domain (x) has exactly one value of the range (y). • Ex. Give the domain and range of the relation graphed at the right. • Is the relation a function?

  8. Ways to show a relation is a function • Mapping Diagram • Vertical-line test

  9. Mapping Diagram • Write the elements of the domain in one region and the elements of the range in another region. Draw arrows to show how each element from the domain is paired with each element in the range. • Ex. • Is the relation a function?

  10. Examples Determine if the relation is a function.

  11. Vertical-line Test • A visual way to tell whether the relation is a function by graphing the relation on a coordinate plane. If a vertical line passes through two or more points on the graph, then the relation is not a function. • Examples Is Not a function Is a function

  12. More Examples • Determine if the relation is a function.

  13. Function Notation

  14. Evaluate the functions for the given values.

  15. Example Suppose 54.

  16. Homework Pp 59-60, #1, 5, 8, 9, 12-21, 22, 25, 28, 31, 32, 36, 38, 40-45, 46, 50-54 (3 graphs)

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