1. Introduction to Functions
Indicator 4

2. Definitions
Graphs – a graph is used to help visually represent the relationship between 2 variable quantities as they both change
Independent Variables – are the input values
Dependent Variables – variables that change in response to other variables. Also called the output values

3. Ex 1: What are the variables in each graph
Ex 1: What are the variables in each graph? Describe how the variables are related at various points on the graph.

4. Ex 2: Match the graph with its related table

5. Ex 3: Sketch the graph of each situation.
The temperature warms up during the day and then decreases at night.
Your distance from school as you leave your house and walk to school. Your distance from school as you leave school and walk to your house.

6. Definitions Relation – The pairing of numbers
Domain – the x-values of a relation, also the independent Variables
Range – the y-values of a relation, or the dependent Variables
Functions – a relation that pairs each input with exactly 1 output value
Linear Function – a function whose graph is a nonvertical line
Vertical Line Test – a way to help determine if the graph of a relation is a function

7. Ex 5: For each table, Find the domain and Range, and determine whether the relationship is a function. Then represent the relationship using words and a graph.

8. Ex 6: Does the set of ordered pairs {(0, 2), (1, 4), (3, 5), and (1, 8)} represent a function? Represent the function with a mapping diagram. Explain.

9. Ex 7: You can make a bubble solution by mixing 1 cup of liquid soap with 4 cups of water. Represent the relationship between the cups of liquid soap and the cups of bubble solution made using a table, and a graph. Is the amount of bubble solution made a function of the amount of liquid soap used? Explain

10. Ex 8: Is the relation a function? Use the vertical line test
a. {(4, 2), (1, 2), (0, 1), (-2, 2), (3, 3)} b. {(0, 2), (1, -1), (-1, 4), (0, -3), (2, 1)}

11. Ex9: The function T(x) = 65x represents the number of words t(x) that Rachel can type in x minutes. How many words can she type in 7 minutes

12. Ex 10: What is the range of f(x)=3x-2 with domain {1, 2, 3, 4}?

13. Ex 11: Lorena has 4 rolls of ribbon to make party favors
Ex 11: Lorena has 4 rolls of ribbon to make party favors. Each roll can be used to make 30 favors. The function f(r) = 30r represents the number of favors f(r) that can be made with r rolls. What is a reasonable domain and range of the function? What is the graph of the function?