Intermediate Algebra Chapter 2

1. Intermediate AlgebraChapter 2 • The • Coordinate Plane • and • Functions

2. Babe Didrikson Zaharias, athlete • “The formula for success is simple: Practice and concentration, then more practice and more concentration.”

3. Section 2.1 • Rectangular Coordinate system • Plotting points • Intercepts • Graphing Calculator

4. Graphing Calculator Keys • 2nd QUIT , Window, Arrow Keys • Y= • Clear • ZOOM 6 – Standard • ZOOM 8 – Integer • TRACE • ZOOM IN ZOOM OUT

5. Calculator Keys • [VARS] • [Y-VARS] • Evaluating function • Try Y = 3x – 2 for x =5

6. Intermediate Algebra 2.1 • The Graph of an Expression

7. Repeated Evaluation of expression • Enter expression in [Y=] • [VARS][Y-VARS] • [1:Function] • [1:Y][ENTER]

8. Section 2.2 Evaluate Expression • Enter expression in Y screen • And produce table • 2nd TBLSET • 2nd TABLE

9. Graphing calculator keys • [Y=] • [Window] • [Graph] • [Trace] • [Zoom] • [Zoom Integer]

10. Setting Window • By Hand • Zoom • 6:Zstandard • 8:Zinteger • X[-9.4,9.4] Y[-10,10] friendly window

11. Zbox • Zoom In • Zoom Out • Z Decimal

12. Modeling • Algebraic Models of situations are not perfect. • Values of dates and variables need to be examined carefully • Models can give predictions • Some models are better than others

13. Section 2.2 • Relations and Functions • ***********************

14. Jackie Joyner-Kersee - athlete • “It is better to look ahead and prepare than to look back and regret.”

15. Relation • A set of Ordered Pairs. • {1,2,(3,4)} • {(2,3),(2,4)}

16. Domain • The set of first components of ordered pairs. • {(1,2),(3,4)} • Domain = {1,3}

17. Range • The set of second components of ordered pairs. • {(1,2),(3,4)} • Range = {2,4}

18. Function • Is a relation in which no two ordered pairs have the same first components. • {(1,2),(3,4)}

19. Vertical Line Test • The graph of a relation represents a function if and only if no vertical line intersects the graph at more than one point

20. Interval Notation • (2,5) • (2,5] • [2,5] • [2,5)

21. Section 2.2 • Function Notation • and • Evaluation

22. Functional Notation • f(x) read “f of x” • Name of the function is f • x is the domain element • f(x) is the value of the range

23. Calculator evaluation • Table • Y = • YVARS • Program Evaluate • Plug In • Store feature

24. Intermediate Algebra 2.3 • Analysis • of • Functions

25. Lou Holtz – football coach • “No one has ever drowned in sweat.”

26. Analysis of Functions Odell • Maximums • Minimums • Intercepts - zero • Points of Intersection-zero • Domain • Range

27. Absolute Maximum • Y coordinate of the highest point of the graph of the function

28. Absolute Minimum • Y-coordinate of the lowest point of the graph of the function.

29. Local Maximum • Highest point in a “neighborhood” • Local Minimum • Lowest point in a “neighborhood.”

30. X intercept • A point at which the graph intersects the x-axis. • At this point y = 0 • [CALC]2:zero

31. Y-Intercept • A point at which the graph intersects the y-axis. • At this point x = 0. • Calculator – many times can be found using trace

32. Points of Intersection • The point(s) at which the two graphs of two function on the same set of axes intersect each other.

33. Calculator Keys • 2nd CALC • ZERO • MINIMUM • MAXIMUM • INTERSECT • VALUE

34. Study Groups are Useful

35. Unknown author • “Today, be aware of how you are spending your 1,440 beautiful moments, and spend them wisely.”

36. Intermediate AlgebraChapter 2 • Properties • of • Lines

37. Intermediate 2.3 • Linear Equations • In • Two Variables

38. Def: Linear Equation • A linear equation in two variables is an equation that can be written in standard form ax + by = c where a,b,c are real numbers and a and b are not both zero.

39. Def: Solution of linear equation in two variables • A solution of a linear equation in two variables is a pair of numbers (x,y) that satisfies the equation. • Ex:{(3,4)}

40. Def: Intercepts • y-intercept – a point where a graph intersects the y-axis. • x-intercept is a point where a graph intersects the x-axis.

41. Procedure to find intercepts • To find x-intercept • 1. Replace y with 0 in the given equation. • 2. Solve for x • To find y-intercept • 1. Replace x with 0 in the given equation. • 2. Solve for y

42. Find solutions to Equations with 2 variables • 1. Choose a value for one of the variables • 2. Replace the corresponding variable with you chosen value. • 3. Solve the equation for the other variable.

43. Horizontal Line • y = constant • Example: y = 4 • y-intercept (0,4) • Function – no x intercept

44. Vertical Line • x = constant • Example x = -5 • x-intercept (-5,0) • No y intercept • Not a function

45. Intermediate 2.4 • Slope of a Line

46. Objective: • Given two points, determine the slope of a line.

47. Slope

48. Slope

49. Horizontal line • y = constant • Slope is 0 • Examples: y = 5 • y = -3 • Can be done with calculator.

50. Vertical Line • x=constant • Undefined slope • Examples: • x =2 • x = -3 • Not graphed by calculator