1. Section 7.1: Functions and Representations of Functions

2. 7.1 Lecture Guide: Functions and Representations of Functions Objective: Determine whether a relation is a function. Objective: Determine the domain and range of a function.

3. Function A function is a correspondence that matches each input value with exactly one value of the output variable. The set of all possible input values is called the domain of the function or the set of independent values. The set of all output values is called the range of the function or the set of dependent values.

4. 1. Classify each correspondence as either a function or as a correspondence that is not a function. For each function identify the domain and range. (a)(b) (c)

5. 2. Give the domain and range of the following function, and convert this function given in ordered pair notation to mapping notation and then graph this function. Ordered-Pair NotationDomain and Range Mapping Notation Graph

6. Domain and Range from a Graph Domain: The domain of a function is the projection of its graph onto the _____-axis. Range: The range of a function is the projection of its graph onto the _____-axis.

7. Give the domain and range of each graph: 3. Domain: Range:

8. Give the domain and range of each graph: 4. Domain: Range:

9. Give the domain and range of each graph: 5. Domain: Range:

10. Give the domain and range of each graph: 6. Domain: Range:

11. Vertical Line Test A graph represents a function if it is impossible to have any vertical line intersect the graph at more than _________________________ point.

12. Use the vertical line test to determine whether each graph represents a function: 7. Function? Yes / No 8. Function? Yes / No

13. Objective: Use function notation. Function Notation The expressionis read as “f of x” or “the value of f at x.” The variable x represents an input value from the domain, and is the corresponding output value.

14. Graph each linear function: 9. EvaluateOrdered PairsGraph of Line

15. Graph each linear function: 10. EvaluateOrdered PairsGraph of Line

16. 11. Note that these functions are in the form which is called the _________________________ - _________________________ form of a line.

17. 12. Use the table to answer the following questions: (a) Evaluate (b) Find the value of x when (c)Evaluate (d)Find the value of x when

18. 13. Use the table to answer the following questions: (a) Evaluate (b) Find the value of x when (c)Evaluate (d)Find the value of x when

19. A graphing calculator has been used to graph each function. Use the graph to determine the domain and range of each function. 14. Domain: ____________ Range: ____________

20. A graphing calculator has been used to graph each function. Use the graph to determine the domain and range of each function. 15. Domain: ____________ Range: ____________