1. College Algebra Chapter 2 Functions and Graphs
Section 2.3
Functions and Relations
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2. Concepts Determine Whether a Relation is a Function
Apply Function Notation
Determine x- and y-intercepts of a Function Defined by y = f(x)
Determine Domain and Range of a Function
Interpret a Function Graphically

3. Concept 1 Determine Whether a Relation is a Function

4. Determine Whether a Relation is a Function (1 of 2)
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 (2 of 2)
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. Skill Practice 1 For the table shown.
Write the set of ordered pairs that defines the relation.
Write the domain.
Write the range. X 3 -2 5 1 y -4

7. Examples 1, 2 Determine if the relation defines y as a function of x
Solution:
{(2,3)}, {(2,4)}, {(3,5)}
{(2,3)},{(2,4)} → diff. y same x
No, not a function.
{(1,3)}, {(2,3)}, {(3,5)}
Yes

8. Skill Practice 2
Determine if the relation defines y as a function of x.
{(8,4), (3,-1), (5,4)}
{(-3,2), (9,5), (1,0), (-3,1)}

9. Example 3 Determine if the relation defines y as a function of x
Solution: Yes

10. Examples 4, 5 Determine if the relation defines y as a function of x
y = 2x + 6
Solution:
Yes
Solution:
Yes

11. Examples 6 – 8 (1 of 2)
Determine if the relation defines y as a function of x
x = 7- y
Solution:
Y=7-x
Yes

12. Examples 6 – 8 (2 of 2)

13. 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.

14. Examples 9 – 11 (1 of 3)
Determine if the graph defines y as a function of x Solution: No

15. Examples 9 – 11 (2 of 3)
yes

16. Examples 9 – 11 (3 of 3)
Yes

17. Skill Practice 3
Determine if the given relation defines y as function of x.

18. Skill Practice 4
Determine if the relation defines y as a function of x.
|y+1|

19. Concept 2 Apply Function Notation

20. Example 12 (1 of 2)

21. Example 12 (2 of 2)

22. Example 13
Solution:

23. Skill Practice 5
Evaluate the function defined by h(x)=4x-3 for the given values of x.
h(-3)
h(-1)
h(0)
h(1)
h(3)

24. Skill Practice 6 Evaluate the function defined by
for the given values of x.
f(t)
f(a+h)

25. Concept 3 Determine x- and y-intercepts of a Function Defined by y = f(x)

26. 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).

27. Example 14
Find the x-and y-intercepts.
Solution:

28. Example 15
Find the x-and y-intercepts. g(x) = 3 - |x|
Solution:

29. Example 16
Find the x-and y-intercepts.
Solution:

30. Skill Practice 7
Find the x-and y-intercepts of the function defined by f(x) =|x|-5.

31. Concept 4 Determine Domain and Range of a Function

32. 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.

33. Example 17
Determine the domain and range for the function Solution:

34. Example 18
Determine the domain and range for the function
Solution:

35. Example 19
Determine the domain and range for the function Solution:

36. Example 20
Determine the domain and range for the function Solution:

37. Skill Practice 8
Determine the domain and range for the functions shown.

38. Skill Practice 9
Write the domain of each function in interval notation.

39. Concept 5 Interpret a Function Graphically

40. Example 21 (1 of 2) Use the graph of y=f(x) to answer the following:
Solution:
f(-3)=-3
f(0)=2
find all x for which f(x)=-1
y=-1 x=-1

41. Example 21 (2 of 2) Find all x for which f(x) f(x)=1 y=-1 x=2
Determine the x-intercept.
No x-integer
Determine the y-intercept.
(0,2)
Determine the domain of f
Determine the range of f.

42. Skill Practice 10 (1 of 2) Use the function f pictured to find: f(-2)
All x for which f(x) =3.
All x for which f(x)=1.
The x-intercept(s).
The y-intercept.
The domain of f.
The range of f.

43. Skill Practice 10 (2 of 2)