1. 2- 4-’13 What have we reviewed so far? Real Numbers and Their Porperties. Equations and Inequalities with one variable. Functions and Special Functions. Inverse Functions.

2. Review: 2. If w = 4, x = -12, y = 64, z = -3 Find: 3. Simplify : 12b – 9 + 4b – 7 b +1 =

3. Review: 4. Solve and graph a) 4x  1  x  10 b) 13 – (2c + 2) > 2(c + 2) + 3c 5. Solve and check: a) 3(x – 6) = 4(x + 2) – 21 b) 2(4x + 1) - 2x = 9x - 1

4. Review 2-5-’13 Let see the greatest integer function:

5. 6. The Speedy-Fast Parcel Service charges for delivering packages by the weight of the package. If the package weighs less than 1 pound, the cost of delivery is $2. If the package weighs at least 1 pound, but less than 2 pounds, the cost is $3.50. For each additional pound, the cost of delivery increases $1.50. Graph the function that describes this relationship. This is an example of an application of the ___________ function. The equation that describes this function is: f(x) = 1.50 [x] + 2

6. Graph the function x [x] f(x) 0.102.00 0.502.00 0.702.00 1.013.50 1.413.50 1.913.50 2.425.00 2.725.00 3.136.50 3.736.50

7. 7. Absolute Value Functions Graph y = |x| - 3 by completing the t-table: x y -2 0 1 2

8. 8. Piecewise Functions 2 is where the graph changes. Less then 2 uses 3x + 2 Greater then 2 uses x - 3

9. We can and should put in a few x into the function If f(0) we use 3x + 2, then 3(0) + 2 = 2 If f(3) we use x – 3, then (3) – 3 = 0 The input tell us what function to use.

10. Piecewise Functions So put in an x where the domain changes and one point higher and lower (2, 8) (2, -1)

11. Inverse Functions Please let’s check the organizers you received on Thursday

12. Lesson 2.5: Scatter Plots Standards: F.IF.7 Objective: Determine the correlation of a scatter plot

13. F. IF. 5 Relate the domain of a function to the graph and, whether applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in factory, then the positive integers would be an appropriate domain for the function. Emphasize the selection of a model function based on based on behavior of data and context.

14. Standards for Mathematical Practices.  1. Make sense of problems and persevere in solving them.  2. Reason abstractly and quantitatively.  3. Construct viable arguments and critique the reasoning of others.  4. Model with mathematics.  5. Use appropriate tools strategically.  6. Attend to precision.  7. Look for and make use of structure.  8. Look for and express regularity in repeated reasoning.

15. Essential Question: How do I calibrate my axes on a coordinate plane within the context of the data?

16. Scatter Plot A scatter plot is a graph of a collection of ordered pairs (x,y). The graph looks like a bunch of dots, but some of the graphs are a general shape or move in a general direction.

17. Positive Correlation If the x-coordinates and the y-coordinates both increase, then it is POSITIVE CORRELATION. This means that both are going up, and they are related.

18. Positive Correlation If you look at the age of a child and the child’s height, you will find that as the child gets older, the child gets taller. Because both are going up, it is positive correlation. Age12345678 Height “ 2531343640414755

19. Negative Correlation If the x-coordinates and the y- coordinates have one increasing and one decreasing, then it is NEGATIVE CORRELATION. This means that 1 is going up and 1 is going down, making a downhill graph. This means the two are related as opposites.

20. Negative Correlation If you look at the age of your family’s car and its value, you will find as the car gets older, the car is worth less. This is negative correlation. Age of car 12345 Value$30,000$27,000$23,500$18,700$15,350

21. No Correlation If there seems to be no pattern, and the points looked scattered, then it is no correlation. This means the two are not related.

22. No Correlation If you look at the size shoe a baseball player wears, and their batting average, you will find that the shoe size does not make the player better or worse, then are not related.

23. Scatterplots Which scatterplots below show a linear trend? a) c)e) b) d)f) Negative Correlation Positive Correlation Constant Correlation

24. Year Sport Utility Vehicles (SUVs) Sales in U.S. Sales (in Millions) 1991 1992 1993 1994 1995 1996 1997 1998 1999 0.9 1.1 1.4 1.6 1.7 2.1 2.4 2.7 3.2 1991 1993 1995 1997 1999 1992 1994 1996 1998 2000 x y Year Vehicle Sales (Millions) 5432154321 Objective - To plot data points in the coordinate plane and interpret scatter plots.

25. 1991 1993 1995 1997 1999 1992 1994 1996 1998 2000 x y Year Vehicle Sales (Millions) 5432154321 Trend is increasing. Scatterplot - a coordinate graph of data points. Trend appears linear. Positive correlation. Predict the sales in 2014.

26. Plot the data on the graph such that homework time is on the y-axis and TV time is on the x-axis.. Student Time Spent Watching TV Time Spent on Homework Sam Jon Lara Darren Megan Pia Crystal 30 min. 45 min. 120 min. 240 min. 90 min. 150 min. 180 min. 150 min. 90 min. 30 min. 90 min.

27. Plot the data on the graph such that homework time is on the y-axis and TV time is on the x-axis. TVHomework 30 min. 45 min. 120 min. 240 min. 90 min. 150 min. 180 min. 150 min. 90 min. 30 min. 120 min. 90 min. Time Watching TV Time on Homework 30 90 150 210 60 120 180 240 240 210 180 150 120 90 60 30

28. Describe the relationship between time spent on homework and time spent watching TV. Time Watching TV Time on Homework 30 90 150 210 60 120 180 240 240 210 180 150 120 90 60 30 Trend is decreasing. Trend appears linear. Negative correlation.

29. Correlation Coefficient The quantity r, called the linear correlation coefficient, measures the strength and the direction of a linear relationship between two variables. The linear correlation coefficient is sometimes referred to as the Pearson product moment correlation coefficient in honor of its developer Karl Pearson.

30. Correlation Coefficient The value of r is such that -1 < r < +1. The + and – signs are used for positive linear correlations and negative linear correlations, respectively. A correlation greater than 0.8 is generally described as strong, whereas a correlation less than 0.5 is generally described as weak

31. Coefficient of Determination r^2 The coefficient of determination, r 2, is useful because it gives the proportion of the variance (fluctuation) of one variable that is predictable from the other variable. It is a measure that allows us to determine how certain one can be in making predictions from a certain model/graph. The coefficient of determination is the ratio of the explained variation to the total variation.

32. Coefficient of Determination r^2 The coefficient of determination is such that 0 < r 2 < 1, and denotes the strength of the linear association between x and y. The coefficient of determination represents the percent of the data that is the closest to the line of best fit. For example, if r = 0.922, then r 2 = 0.850, which means that 85% of the total variation in y can be explained by the linear relationship between x and y (as described by the regression equation). The other 15% of the total variation in y remains unexplained. The coefficient of determination is a measure of how well the regression line represents the data.

33. Interpolation and Extrapolation  Interpolation Interpolation is the process of obtaining a value from a graph or table that is located between major points given, or between data points plotted. A ratio process is usually used to obtain the value.  Extrapolation Extrapolation is the process of obtaining a value from a chart or graph that extends beyond the given data. The "trend" of the data is extended past the last point given and an estimate made of the value.