The document discusses domain and range of graphs. It defines domain as all the x-values and range as all the y-values of a graph. It provides examples of determining the domain and range from graphs, describing whether they include or exclude endpoint values and how to write the domain and range in inequality notation.

1. Domain and Range Part 1

2. Objectives To learn about different notation on graphs To learn how to find the domain and range of a graph

3. Quick Review What are some words that we use with domain : Input X values What are some words that we use with range ? output y values

4. Previously we have found the domain and range if we were given points on a graph, or order pairs, or don’t forget the mapping diagram. Now we are going to find domain and range on a continuous graph. USE THIS PowerPoint TO HELP WITH THE LAST PAGE IN YOUR FUNCTIONS PACKET!!!!!!!!!!!!!!!!!!!!!!!!!

5. Graphing Notation An open circle means it does not include that point A closed circle means it does include the point An arrow means it keeps going that direction endlessly x y x y

6. Domain and Range Domain is all the ___ values The x values go from ______ to _______ So domain is how far left and right it goes Range is all the ____ values The y values go ______ and ______ So range is how far up and down it goes x left right y up down

7. Domain and Range The domain is all possible x values The possible x values are those between -2 and 4 -2 4 Domain: -2 ≤ x ≤ 4 The Range is all possible y values 5 2 The possible y values are those between 2 and 5 Range: 2 ≤ y ≤ 5 x y

8. Domain and Range The domain is all possible x values The possible x values are those between -6 and 8 Domain: -6 ≤ x < 8 The Range is all possible y values The possible y values are those between -7 and 4 Range: -7 ≤ y ≤ 4 -6 8 An open circle means not including that point -7 4 x y

9. Domain and Range The domain is all possible x values The possible x values are those between -4 and 5 Domain: -4 ≤ x ≤ 5 The Range is all possible y values The possible y values are those between 2 and 7 Range: 2 < y ≤ 7 2 7 An open circle means not including that point -4 5 x y

10. Domain and Range The domain is all possible x values The possible x values are those less than or equal to 6 Domain: x ≤ 6 The Range is all possible y values The possible y values are those less than or equal to 4 Range: y ≤ 4 6 4 x y

11. Domain and Range The Domain is all possible x values The x values are any numbers Domain: All reals The Range is all possible y values 3 The y values are any numbers less than or equal to 3 Range: y ≤ 3 x y

12. Domain and Range The Domain is all possible x values The x values are any numbers greater than or equal -5 Domain: x ≥ -5 The Range is all possible y values -5 The y values are any numbers Range: y is all reals x y

13. Conclusion Domain is all the ___ values The x values go from ______ to _______ Range is all the ____ values The y values go ______ and ______ x left right y up down