1. College Algebra Chapter 2 Functions and Graphs
Section 2.3
Functions and Relations

2. 1. Determine Whether a Relation is a Function
2. Apply Function Notation
3. Determine x- and y-intercepts of a Function Defined by y = f(x)
4. Determine Domain and Range of a Function
5. Interpret a Function Graphically

3. Determine Whether a Relation is a Function
Definition of a Relation:
A set of ordered pairs (x, y) is called a relation in
x and y.
The set of x values in the ordered pairs is called the domain of the relation.
The set of y values in the ordered pairs is called the range of the relation.

5. Determine Whether a Relation is a Function
Definition of a Function:
Given a relation in x and y, we say that y is a function of x if for each value of x in the domain, there is exactly one value of y in the range.

6. Examples 1, 2:
Determine if the relation defines y as a function of x

7. Example 3:
Determine if the relation defines y as a function of x x y –2 6 

8. Examples 4, 5:
Determine if the relation defines y as a function of x

9. Examples 6 – 8:
Determine if the relation defines y as a function of x

10. Determine Whether a Relation is a Function
Vertical Line Test:
A graph defines y as a function of x if no vertical line intersects the graph in more than one point.

11. Examples 9 – 11:
Determine if the graph defines y as a function of x 9.
10.
11.

14. 1. Determine Whether a Relation is a Function
2. Apply Function Notation
3. Determine x- and y-intercepts of a Function Defined by y = f(x)
4. Determine Domain and Range of a Function
5. Interpret a Function Graphically

15. Example 12:
Evaluate for the given values of x.

16. Example 13:
Evaluate for the given values of x.

17. 1. Determine Whether a Relation is a Function
2. Apply Function Notation
3. Determine x- and y-intercepts of a Function Defined by y = f(x)
4. Determine Domain and Range of a Function
5. Interpret a Function Graphically

18. Determine x- and y-intercepts of a Function Defined by y = f(x)
Given a function defined by y = f (x):
The x-intercepts are the real solutions to the equation
f (x) = 0.
The y-intercept is given by f (0).

19. Example 14:
Find the x-and y-intercepts.

20. Example 15:
Find the x-and y-intercepts.

21. Example 16:
Find the x-and y-intercepts.

22. 1. Determine Whether a Relation is a Function
2. Apply Function Notation
3. Determine x- and y-intercepts of a Function Defined by y = f(x)
4. Determine Domain and Range of a Function
5. Interpret a Function Graphically

23. Determine Domain and Range of a Function
Given a relation defining y as a function of x, the domain is the set of x values in the function, and the range is the set of y values in the function.

24. Example 17:
Determine the domain and range for the function
Domain: _______________
Range: ________________

25. Example 18:
Determine the domain and range for the function
Domain: _______________
Range: ________________

26. Example 19:
Determine the domain and range for the function
Domain: _______________
Range: ________________

27. Example 20:
Determine the domain and range for the function
Domain: _______________
Range: ________________

28. 1. Determine Whether a Relation is a Function
2. Apply Function Notation
3. Determine x- and y-intercepts of a Function Defined by y = f(x)
4. Determine Domain and Range of a Function
5. Interpret a Function Graphically

29. Example 21:
Use the graph of to answer the following:

30. Example 21 continued:
Use the graph of to answer the following:

31. Example 21 continued:
Use the graph of to answer the following:
Determine the
x-intercept.
Determine the
y-intercept.

32. Example 21 continued:
Use the graph of to answer the following:
Determine the
domain of f.
Determine the
range of f.