1. GRAPHING EQUATIONS BY TYPE AND WITH POINTS By Mr. Barnard

2. OBJECTIVE: Know the shape of a graph from its equation and sketch a graph by plotting points.

3. LIFE EXPECTANCY

4. AGE OF MOTHER WITH FIRST BORN

5. PROBABILITY OF FIRST MARRIAGE

6. BIRTHS TO UNMARRIED WOMEN

7. TYPES OF GRAPHS

8. Linear: y = x

9. Quadratic: y = x 2

10. Cubic: y = x 3

11. Square Root:

12. Logarithms: y= logx y= lnx

13. y= sinx y= cosx Trigonometry:

14. y= tanx y= cotx Trigonometry:

15. y= secx y= cscx

16. Absolute Value: y = |x|

17. COORDINATE PLANE

18. X-axis Y-axis Quadrants Origin III III IV Ordered Pair

19. PRACTICE GRAPHING USE YOUR WHITE BOARD, ERASER, AND MARKER

20. y = 5x - 2

21. y = 2x 2 + 1

23. y = 3x 3 – 2x 2 - 1

24. y = 5sin2x Plug in radian values for x!

25. INTERCEPTS

26. X-intercept Y-intercept Values where a line or curve crosses the x-axis. (y = 0) Values where a line or curve crosses the y-axis. (x = 0)

27. Determine the x & y intercepts for:  y = x 2 - 1  y = x  y = 6x 3 + 4x 2

28. Which equation matches the graph? y= 3x – 5 y= 2x 2 – 5 y= 5x 2 + 1 y= x3 x3 - 5

29. SYMMETRY The quality of having balance or exact parts of a figure on either side of an axis.

30. EXAMPLES OF SYMMETRY

31. MORE EXAMPLES OF SYMMETRY

34. LOOK AROUND… SYMMETRY… IT’S ALL AROUND YOU RIGHT NOW!

35. X-axis symmetry: can replace y with –y and produce the same equation. Y-axis symmetry: can replace x with –x and produce the same equation. Origin symmetry: can replace x with –x AND y with –y and produce the same equation. TYPES OF SYMMETRY

36. Prove and disprove the type of symmetry for each:  y = x 2 + 4  y = -x 3 - 1  y = x 4 - 2

37. Even function: symmetric with the y-axis Odd function: symmetric with the origin What type of function is symmetric with the x-axis?

38. Using y = x 3 - x 2, determine the x-intercepts (show evidence) y-intercepts (show evidence) type of symmetry (prove and disprove) graph (use intercepts, symmetry, & other points

39. SKETCH A GRAPH: Quadratic Equation X-axis Symmetry X-intercept at –2 Y-intercept at 3 (3, 4)

40. SKETCH A GRAPH: Quadratic Equation Y-axis Symmetry X-intercept at 3 Y-intercept at 2 (-5, -2)

41. SKETCH A GRAPH: Cubic Equation Origin Symmetry X-intercept at –4 Y-intercept at 0 (-2, 2) and (-6, -4)

42. SUGGESTED PRACTICE: Page 8 (1-12, 20, 32, 39-42, 44-47, 51, 54)