1. Unit 1: Functions Sec1: Relations, Functions, Domain and Range Algebra II

2. Goals/Objectives Essential Question: Essential Question: How do you solve, graph, and apply linear functions to predict and solve real world problems?How do you solve, graph, and apply linear functions to predict and solve real world problems? Objectives: Objectives: Students will identify functions and relations.Students will identify functions and relations. Students will identify the domain and range of a function or relation.Students will identify the domain and range of a function or relation. Students will graph linear equations.Students will graph linear equations.

3. Relations A relation is a mapping, or pairing, of input values with output values. A relation is a mapping, or pairing, of input values with output values. A relation is a function if there is exactly one output for each input. A relation is a function if there is exactly one output for each input. It is NOT a function if at least one input has more than one output It is NOT a function if at least one input has more than one output

4. Domain and Range The domain is the horizontal width of the graph ( all x- values). The range is the vertical height of the graph ( all y- values).

5. Input Output -3 3 1-2 4 1 4 Identify the Domain and Range. Then tell if the relation is a function for the points (-3, 3), (1, -2), (1, 1) and (4, 4). Domain = {-3, 1,4} Range = {3,-2,1,4} Function? No: input 1 is mapped onto Both -2 & 1 Notice the set notation!!!

6. Identify the Domain and Range. Then tell if the relation is a function for the points (-3, 3), (1, 1), (3, 1) and (4, -2). Input Output -3 3 1 3 -2 4 Domain = {-3, 1,3,4} Range = {3,1,-2} Function? Yes: each input is mapped onto exactly one output

7. Vertical Line Test You can use the vertical line test to visually determine if a relation is a function. You can use the vertical line test to visually determine if a relation is a function. Slide any vertical line (pencil) across the graph to see if any two points lie on the same vertical line. Slide any vertical line (pencil) across the graph to see if any two points lie on the same vertical line. If there are not two points on the same vertical line then the relation is a function. If there are not two points on the same vertical line then the relation is a function. If there are two points on the same vertical line then the relation is NOT a function If there are two points on the same vertical line then the relation is NOT a function

8. Graphing Relations Graph the relations in the previous examples on 2 separate graphs. Graph the relations in the previous examples on 2 separate graphs. Plot the points Plot the points Do the Vertical Line Test to determine if the relation is a function. Do the Vertical Line Test to determine if the relation is a function.

9. (-3,3) (4,4) (1,1) (1,-2) Use the vertical line test to visually check if the relation is a function. Function? No, Two points are on The same vertical line.

10. (-3,3) (4,-2) (1,1) (3,1) Use the vertical line test to visually check if the relation is a function. Function? Yes, no two points are on the same vertical line

11. Graphing and Evaluating Functions Many functions can be represented by an equation in 2 variables: Many functions can be represented by an equation in 2 variables: y=x²-7 and y = 2x + 1 y=x²-7 and y = 2x + 1 A. Is the graph a function? A. Is the graph a function? B. What is the domain of the function? B. What is the domain of the function? C. What is the range of the function? C. What is the range of the function?

12. Assignment Handout Relation and Functions