1. CHAPTER 2 Section 2.1

2. Objectives To graph a relation, state its domain and range, and determine if it is a function. To find values of functions for a given elements of the domain. Use a graphing calculator to graph linear equations Why is it important? You can use relations to solve problems involving geography, forestry, and sports.

3. Coordinate System What is a coordinate system? A system that uses coordinates to establish position. What are some examples? Graphs Latitude/Longitude

4. Cartesian Coordinate Plane What are the different components of this coordinate plane? x-axis y-axis origin ordered pairs quadrants (x, y) III III IV

5. Relation A set of ordered pairs, (x, y), forms a relation. Domain- all the x values Range – all the y values

6. Mapping 7 2 4 -3 3 6 8 {(2, 3), (-4, 8), (2, 6), (7, -3)} What is the domain? Range

7. Functions A function is a special type of relation in which each element of the domain is paired with exactly one element from the range. Which of the following are functions?

8. Vertical Line Test Which relations were functions? What is the vertical line test?

9. Continuous Function What do we think it means? Contains points that are connected *This means NO gaps

10. Discrete Function What do we think it means? Contains points that are NOT connected

11. Examples State Whether each relation is a function or not. 3 2 -6 1515 xy 5-2 10-2 15-2 20-2 (4,-1) (2,3) (2,2) (3,1) Function Not a Function

12. Examples For each relation: - state the domain and range. - identify whether it is a function or not - state whether it is discrete or continuous a) {(7, 8), (7, 5), (7, 2), (7,-1)} b) y = -2x + 1 c) {(6, 2.5), (3, 2.5), (4, 2.5)} Domain: {7}; Range: {8, 5, 2, -1}; Not a Function Domain: All Reals; Range: All Reals; Function; Continuous Domain: {3, 4, 6}; Range: {2.5}; Function; Discrete

13. Examples Find f(5) if f(x) = x 2 – 3x f(5) = 5 2 – 3(5) f(5) = 25 – 15 f(5) = 10 Find h(-2) if h(x) = x 3 + 1 h(-2) = (-2) 3 + 1 h(-2) = -8 + 1 h(-2) = -7

14. Graphing Technology On your graphing calculator, graph y-2x = 3 How do we do this? 1. Put function in “y =” form. y = 2x + 3 2. Enter Y = 2x + 3 Zoom (#6) GRAPH 3. How can we describe the graph?

15. Graphing Technology Now try y = -x + 14 What happens?

16. Exercises On the back of your notes do 1-8 (even) on page 72.

17. Exit Slips Remember our objectives: To graph a relation, state its domain and range, and determine if it is a function. To find values of functions for a given elements of the domain. Use a graphing calculator to graph linear equations Use them to answer your exit slip questions.