2.4 Graphing Inequalities

Transcription

1 .4 Graphing Inequalities

2 Why We Need This Our applications will have associated limiting values - and either we will have to be at least as big as the value or no larger than the value.

3 Why We Need This Our applications will have associated limiting values - and either we will have to be at least as big as the value or no larger than the value. These situations are represented by inequalities, and when we take all of those in a problem together, we are looking for the common intersection. This will be called the feasible set.

4 Why We Need This Our applications will have associated limiting values - and either we will have to be at least as big as the value or no larger than the value. These situations are represented by inequalities, and when we take all of those in a problem together, we are looking for the common intersection. This will be called the feasible set. The difference between how you would have learned these before and how we will do this here is that we will shade where the inequality is false. You have been taught to always shade where the inequality is true.

5 One Inequality Example Graph y x + 1.

6 One Inequality Example Graph y x + 1. First, we plot the linear function associated with the inequality

7 One Inequality Then, we decide which side of the line satisfies the inequality. The easiest way I know id to use a test point. When the line is does not pass through the origin, I use (0, 0) for the test point.

8 One Inequality Then, we decide which side of the line satisfies the inequality. The easiest way I know id to use a test point. When the line is does not pass through the origin, I use (0, 0) for the test point. y x (0)

9 One Inequality Then, we decide which side of the line satisfies the inequality. The easiest way I know id to use a test point. When the line is does not pass through the origin, I use (0, 0) for the test point. y x (0) This is a false statement. So, we shade the side that contains the test point.

10 One Inequality Then, we decide which side of the line satisfies the inequality. The easiest way I know id to use a test point. When the line is does not pass through the origin, I use (0, 0) for the test point. y x (0) This is a false statement. So, we shade the side that contains the test point

11 One Inequality Then, we decide which side of the line satisfies the inequality. The easiest way I know id to use a test point. When the line is does not pass through the origin, I use (0, 0) for the test point. y x (0) This is a false statement. So, we shade the side that contains the test point. 3 feasible set

12 Two Inequalities Example Graph the given system of inequalities. { y -x+3 y x No difference here - we do the same thing as we just did, just twice.

13 Two Inequalities

14 Two Inequalities (0)

15 Two Inequalities This is a true statement. 0 (0)

16 Two Inequalities The line passes through the origin, so we need to use another point as the test point. Why can t we use the origin?

17 Two Inequalities

18 Two Inequalities The line passes through the origin, so we need to use another point as the test point. Why can t we use the origin?

19 Two Inequalities

20 Two Inequalities Using the point (1,0), we have that 0 (1) 0, which is true.

21 Two Inequalities Using the point (1,0), we have that 0 (1) 0, which is true. Which side do we shade?

22 Two Inequalities

23 Two Inequalities feasible set -3

24 Another Two Inequality Example Example Graph the given system of inequalities. { y x+ y 3x-1

25 Another Two Inequality Example Example Graph the given system of inequalities. { y x+ y 3x-1 Here, we will test both first. Since neither line has the origin as it s y-intercept, we can (0, 0) as test point for each.

26 Another Two Inequality Example Example Graph the given system of inequalities. { y x+ y 3x-1 Here, we will test both first. Since neither line has the origin as it s y-intercept, we can (0, 0) as test point for each. y x + 0

27 Another Two Inequality Example Example Graph the given system of inequalities. { y x+ y 3x-1 Here, we will test both first. Since neither line has the origin as it s y-intercept, we can (0, 0) as test point for each. y x + 0 true

28 Another Two Inequality Example Example Graph the given system of inequalities. { y x+ y 3x-1 Here, we will test both first. Since neither line has the origin as it s y-intercept, we can (0, 0) as test point for each. y x + 0 true y 3x 1 0 1

29 Another Two Inequality Example Example Graph the given system of inequalities. { y x+ y 3x-1 Here, we will test both first. Since neither line has the origin as it s y-intercept, we can (0, 0) as test point for each. y x + 0 true y 3x true

30 Another Two Inequality Example

31 Another Two Inequality Example

32 Another Two Inequality Example

33 Another Two Inequality Example

34 Another Two Inequality Example feasible set -3

35 Three Inequalities Example Graph the given system of inequalities. x + y 4 x y 5 y x 4

36 Three Inequalities

37 Three Inequalities

38 Three Inequalities

39 Three Inequalities

40 Three Inequalities

41 Three Inequalities

42 Three Inequalities feasible set

43 Three Inequalities Example Graph the given system of inequalities. 3x y 6 x + y 5 y

44 Three Inequalities

45 Three Inequalities

46 Three Inequalities

47 Three Inequalities

48 Three Inequalities

49 Three Inequalities

50 Three Inequalities feasible set -4-6

51 Multiple Inequalities Example Graph the given system of inequalities. x 3 1 y 5 x + y 6

52 Multiple Inequalities

53 Multiple Inequalities

54 Multiple Inequalities

55 Multiple Inequalities

56 Multiple Inequalities

57 Multiple Inequalities

58 Multiple Inequalities 6 4 feasible set

59 Multiple Inequalities Example Graph the given system of inequalities. y x + 4 y 3 x x 0, y 0

60 Multiple Inequalities

61 Multiple Inequalities

62 Multiple Inequalities

63 Multiple Inequalities

64 Multiple Inequalities

65 Multiple Inequalities 6 4 f.s