1. 2.4 Graphs of Functions The graph of a function is the graph of its ordered pairs.

2. Graphing a Function by Plotting Points

3. Steps for Graphing an Equation Using a Graphing Utility

6. Ex 1: Graphing a Function by Plotting Points

7. Solution x 0 1 4 9 16 25

8. Solution Contd.

12. Practice Exercise

13. Answer

14. Obtaining Information From Graphs You can obtain information about a function from its graph. At the right or left of a graph, you will find closed dots, open dots, or arrows. An arrow indicates that the graph extends indefinitely in the direction in which the arrow points.

15. Obtaining Information From Graphs A closed dot indicates that the graph does not extend beyond this point and the point belongs to the graph. An open dot indicates that the graph does not extend beyond this point and the point does not belong to the graph.

16. Ex 2: Obtaining Information From a Function’s Graph

17. Solution of part a.

18. Solution of part b.

19. Solution of part c.

20. The Vertical Line Test If any vertical line intersects a graph in more than one point, the graph does not define y as a function of x.

21. Ex 3: Using the Vertical Line Test

22. Solution

23. Increasing Function A function is increasing on an interval if for any x 1 and x 2 in the interval, where x 1 <x 2, then f(x 1 )<f(x 2 ).

24. Decreasing Function A function is Decreasing on an interval if for any x 1 and x 2 in the interval, where x 1 <x 2, then f(x 1 )>f(x 2 ).

25. Constant Function A function is constant on an interval if for any x 1 and x 2 in the interval, where x 1 <x 2, then f(x 1 )=f(x 2 ).

26. Ex 4: Intervals on Which a Function Increases, Decreases, or Is Constant

27. Solution

28. Even Function

29. Odd Function

30. Identifying Even or Odd Functions

31. Solution

32. Solution for part a.

33. Solution for part b.

34. Solution for part c.

35. Even Functions and y-Axis Symmetry

36. Odd Functions and Origin Symmetry

37. Graphs of Common Functions Use a graphing utility to verify the following six graphs.

38. Constant Function Domain: Range: the single number Constant on Even function

39. Identity Function

40. Standard Quadratic Function

41. Standard Cubic Function

42. Square Root Function

43. Absolute Value Function

44. Greatest Integer Function