1. Warm-up
Name the following functions.
Quadratic
Cubic
Absolute Value

2. What characteristics of functions can we find by looking at a graph?
Math III Support
EQ:
What characteristics of functions can we find by looking at a graph?
Standard: MM1A1d

3. Any set of input that has an output
Key Terms
Relation
Any set of input that has an output

4. A relation where EACH input has exactly ONE output
Key Terms
Function
A relation where EACH input has exactly ONE output

5. Key Terms

7. Making an Input-Output Table
Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6

8. Domain and Range Domain: {1, 2, 3, 4, 5, 6} Range:
{1, 3, 6, 10, 15, 21}

9. How do I know if it's a function?
Look at the input and output table – Each input must have exactly one output.
Look at the Graph – The Vertical Line test = NO vertical line can pass through two or more points on the graph

10. Is this a function?
Example 1:
{(3, 2), (4, 3), (5, 4), (6, 5)}

11. Domain & Range Discrete graphs – you just LIST the domain and range
Continuous graphs – you use set notation

12. Domain and Range: Points
Find the domain and range:
{(2, –3), (4, 6), (3, –1), (6, 6), (2, 3)}
domain:  {2, 3, 4, 6}
range:  {–3, –1, 3, 6}

13. Set Notation Uses:
Is used when there is a open dot or the number is NOT included on the graph.
Is used when there is a closed dot or when the number is included on the graph.
Is used when one number is excluded.

14. Domain and Range: Graph

15. Domain and Range: Graph

16. Domain and Range: Graph
Special case: When there is an open circle and closed circle on the same number – go with the closed circle.

17. Domain and Range: Graph

18. Domain and Range: Graph

19. Domain and Range: Graph

20. Maximum or Minimum Point
Max. Point – is the HIGHEST on the graph
Min. Point – is the LOWEST on the graph
(x, y)

21. Maximum or Minimum Value? Where?
Max. Point
(0, 4)

22. Maximum or Minimum Value? Where?
Min. Point
(-1, -9)

23. ZEROS are the same thing as the X-INTERCEPTS.
(x, y)

24. Name the zeros.
(-4, 0)
and
(3, 0)

25. Name the Y-INTERCEPT.
(0, -4)

26. Increasing and Decreasing
To find where the graph is increasing and decreasing trace the graph with your FINGER from left to right.
x-values ONLY!

27. Increasing & Decreasing
MOVE LEFT TO RIGHT
If your finger goes UP, the graph is increasing.
If your finger goes DOWN, the graph is decreasing.
If your finger goes neither up or down…then the graph is CONSTANT.

28. Increasing & Decreasing

29. Increasing & Decreasing

30. Increasing and Decreasing

31. Increasing and Decreasing

32. End Behavior
Is figuring out what the graph is doing as x approaches + and as x approaches -

33. This is when you look at the LEFT and RIGHT “arm” of the graph.
End Behavior
This is when you look at the LEFT and RIGHT “arm” of the graph.

34. End Behavior If the “arm” is going UP, then write +¸.
If the “arm” is going DOWN, then write -¸.
2 special cases: square root & rational

35. Describe the End Behavior

36. Describe the End Behavior

37. Describe the End Behavior

38. Describe the End Behavior

39. Describe the End Behavior

40. Describe the End Behavior

41. Describe the End Behavior

42. Key Terms Relation – Any set of input that has an output
Function – Is a relation that every single input has exactly one output
Input (x-coordinate) is also called the Domain
Output (y-coordinate) is also called the Range

43. Characteristics of Functions
Domain:
Range:
Intervals of Increase and Decrease:
End Behavior:
Max:
Min:

44. Characteristics of Functions
Domain:
Range:
Intervals of Increase and Decrease:
End Behavior:
Max:
Min:

45. Characteristics of Functions
Domain:
Range:
Intervals of Increase and Decrease:
End Behavior:
Max:
Min:

46. Constant Rate of Change
The slope of a nonvertical line is the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line.
Find the slope between (2, 4) and (4, 8).

47. Rate of Change
The rate of change is the ratio of the change of one quantity to a change in another quantity.
Example:
- The table shows the amount of water evaporating from a swimming pool on a hot day. Find the rate of change in gallons with respect to time.

48. Rate of Change
Where is the greatest rate of change on the graph? What is the value?