Algebra 2 Chapter 2 Page 1

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1 Mileage (MPGs) Section. Relations and Functions. To graph a relation, state the domain and range, and determine if the relation is a function.. To find the values of a function for the given element of the domain. I. Relations A. Definitions. Relation. Cartesian Coordinate Sstem a) b) c) d) e) 3. Domain the variable ( ) 4. Range the variable ( ) 5. Function a) A relationship between ( ) and ( ). b) The output ( ) depends on the input ( ). a) A in which each element in the is mapped to and onl element in the. B. Eamples. State the domain and range of the relation shown in the graph. Is the relation a function?. The table shows the average fuel efficienc in miles per gallon for SUVs for several ears. Graph this information and determine whether it represents a function. Is this relation discrete or continuous? Fuel Effecienc of SUVs Year 3. Graph the relation represented b 3 Find the domain and range. Determine whether the relation is a function. - 0 Fuel Year Efficienc (mi/gal) Algebra Chapter Page

2 4. Graph the relation represented b Find the domain and range. Determine whether the relation is a function. 5. Determine whether each relation is a function. a) Mappings: b) Tables: c) Ordered Pairs: ( 5,),(,5),(0,7),(0,9) d) Graphs: ) ) 3) -9 Note: Vertical Line Test II. Function Values and Notation A. Function Notation. 3 8 vs. f ( ) 3 8. Function notation has the advantage of clearl identifing the dependent variable f( ), formerl known as, while at the same time telling ou is the independent variable and that the function itself is called f. 3. Function notation allows ou to be less word. Instead of asking What is the value of that corresponds to? ou can ask What is f ( )? : B. Eamples. If f ( ) 3 3, find f ().. If 3. If 4. If h( ) , find h (.6). 3 f ( ) 3, find f t. g( a) a 5, find g. Homework: p. 64 Basic: -0 all, 45, 47, 55; Etended: 33, 35, 44, 5, 60 Algebra Chapter Page

3 Section. Linear Equations. To identif equations that are linear and graph them.. To write linear equations in standard form. 3. To determine intercepts of a line and use them to graph an equation. Definitions Linear equation an whose graph is a line. Note:. Variable ( variable) graphed on the ais.. Variable ( variable) graphed on the ais. Standard Form where A, B, and C are integers. Function Form Intercepts. -intercept Occurs when the line crosses the. The equals 0. -intercept Occurs when the line crosses the. The equals 0 Characteristics of a Linear Epression. Eamples:. Linear or Not? a. h( ) 3 b. f ( ) 4 c. g(, ) 3 d. f ( ) 3( ) 3. Write in standard form:. Identif A, B, and C Find the - and -intercepts of the line whose equation is given b Graph using intercepts: Alan rides his bike to the store. If Alan stops at a red light along the wa it takes him longer to the reach the store. The time it takes in minutes for Alan to get to the store can be figured b the function t( s) s 5 where s is the number of stops for red lights. 8 4 Complete a table and graph. How long would it take Alan if he stops at 0 red lights? Homework: p. 7 Basic: -5 all, 6, 67; Etended: 39, 4, 47, Algebra Chapter Page 3

4 Section.3 Slope. To determine the slope of a line.. To use the slope and a point to graph a linear equation. 3. To determine if two lines are perpendicular, parallel, or neither. I. Slope A. Definition B. Eamples. Determine the slopes a) (,3) and ( 4,4) b) (7,5) and ( 3,5) c) (5,7) and (5, 3). Find the slope of the line shown at the right. II. Slope as a Rate A. Eamples. In 004, 56,878 students applied to UCLA. In 006, 60,9 students applied. Find the rate of change in the number of students appling for admission from 004 to Refer to the graph to the right, which shows data on the fastest-growing restaurant chain in the U.S. during the time period of the graph. Find the rate of change of the number of stores from 00 to 006. Homework: p. 79 Basic: -8 all, 47, 49, Etended:, 4, 9, 34, 36 Algebra Chapter Page 4

5 Section.4 Writing Linear Equations. To write an equation of a line given the slope and one point or two points. To write an equation of a line that is parallel or perpendicular to the graph of a given equation. A. Slope-intercept form m b. m. b B. Eamples Find the slope-intercept form of the equation with the following givens:. A line that has a slope of 3 5 and passes through the point (5, ). A line that passes through the points (,-3) and (-3,7) 3. A line that passes through the points (-,-5) and (4,-5) 4. As a part-time salesperson, Jean Stock is paid a dail salar plus commission. When her sales are $00, she makes $58. When her sales are $300, she makes $78. a) Write a linear equation to model this situation. (00, 58) (300,78) b) What are Ms. Stock s dail salar and commission rate? c) How much would Jean make in a da if her sales were $500? B. Parallel and Perpendicular Lines. Parallel a) Definition b) A line that passes through the point (3,5) and // 3. Perpendicular a) Definition b) A line that passes through the point (3, ) and 5 Homework: p. 86 Basic: -7 all, 3, 5, 3, 47, 5; Etended: 8, 9, 35, 46 Algebra Chapter Page 5

6 Section.5A Modeling Real-World Data (Manuall). To draw scatter plots and find prediction equations. To solve problems using predictions equations Tpes of correlation. Positive correlation. Negative correlation 3. No correlation A equation can be determined b using a process to the one used to find the of a. The procedure Eamples. The table below shows the approimate percent of students who sent applications to two colleges in various ears since 985. Draw a scatter plot, best fit line, and find an equation that would predict the approimate percent of students who sent applications to two colleges in various ears since 985. Predict the percent of students who will send applications to two colleges in 00. What is the dependent and independent variable and wh? What tpe of correlation does this data have?. Safet The table below shows the approimate percent of drivers who wear seat belts in various ears since 994. What is the dependent and independent variable and wh? Draw a scatter plot and a best fit line. What tpe of correlation does this data have? Find an equation that would predict the approimate percent of drivers who wear seatbelts since 994. What do the slope and - intercept indicate? Predict the percent of drivers who will be wearing seat belts in 00. Homework: p.96 Basic: -6 all, 3, 4, 8; Etended: p Algebra Chapter Page 6

7 Scatter Plots and Regression (prediction) Lines. Entering Data a. EDIT Edit To clear a List:. Go to the top of list. b.. Note: Do not delete lists. Enter the -values in L and -values in L c. QUIT In order to get deleted lists back ou must do the following: SetUpEditor This should restore our lists.. Finding the Prediction Line (Model) a. Calc LinReg(a+b) b. After LinReg(a+b) ou will need to tpe the list he -values are located (usuall L) flowed b a comma and the list where the -values are located (usuall L) followed b another comma and then the location ou want to store the equation (usuall Y). After all is tped in hit Y thru Y9 can be located b doing the following: or Y-VARS Function c. You should get the following. a is our slope and b is our -intercept. Thus our equation is Algebra Chapter Page 7

8 3. Using the model to predict a. Y Y(n) or Y-VARS Function Y Y(n) 4. Graphing Data We do not normall do this step, unless asked to see how well the data fits. a. Clear all equations from that do not pertain to the problem at hand. b. STAT PLOT c. Select on of the Stat Plots d. Make sure the following is selected. Note: If our - or -values are in a different list location ou can alwas change the XList: and YList: locations tping in the new list location. To select put cursor on top of item and hit You can change our mark to our preference. e. QUIT f. ZoomStat Algebra Chapter Page 8

9 Section.5B Modeling Real-World Data (Using a Calculator). To draw scatter plots and find prediction equations. To solve problems using predictions equations Correlation Coefficient ( r ): Shows how well data are modeled b a function. Measures: Eamples. The table shows the median income of U.S. families for the period Use a graphing calculator to make a scatter plot of the data. Find an equation for and graph a line of regression. Then use the equation to predict the median income in 05. Use a graphing calculator to make a scatter plot of the data. Find an equation for and graph a line of regression. Then use the equation to predict the attendance in 05. What is the correlation coefficient? What does this value tell us about our model? Homework: p. 96 Basic: 7- all; Etended: p All problems are to be done using the graphing calculator stats capabilit. Algebra Chapter Page 9

10 Section.6 Special Functions. To identif and graph special functions The Special Functions. Piecewise Function. Absolute Value Function: 3. Greatest Integer Function: ( integer not greater than ) Eample.75 or.9875 or.5 3 Eamples: Graph:, if 3 f( ), if 3 Find the Domain and Range., if f( ) 3, if Find the Domain and Range. Pscholog: One pschologist charges for counseling sessions at the rate of $85 per hour or an fraction thereof. Draw a graph that represents this solution f ( ) 3 Find the Domain and Range. Find the Domain and Range. Homework: p.04 Basic: -4, 7, 0, 0, 5, 5-55 odds; Etended: 8, 34, 49 Algebra Chapter Page 0

11 Section.7 Parent Functions and Transformations. To identif and use parent graphs.. To describe transformations of functions. I. Parent Graphs A. Constant Function: B. Identit Function: C. Absolute Value function: D. Quadratic Function: II. Transformations A. Translation. Horizontal:. Vertical: B. Reflection. Reflection over the -ais:. Reflection over the -ais: C. Dilation. Stretched verticall:. Compressed verticall: D. Eamples. Describe the translation in. Then graph the function.. Describe the translation in 4. Then graph the function. 3. Describe the reflection in. Then graph the function. 4. Describe what transformations to the following function f 4. 4 Then graph the function. Homework: p.3 Basic: -7 all, 9, 0-9 all,, 5, 57; Etended: 33, all, 54 Algebra Chapter Page

12 Section.8 Linear Inequalities. To draw graphs of inequalities with two variables. Boundar Lines. -- or. -- < or > Eamples: Is (, 4) a solution to 3 6? Graph: One tutoring compan advertises that it specializes in helping students who have a combined score on the SAT that is 900 or less. Write an inequalit to describe the combined scores of students who are prospective tutoring clients. Let represent the verbal score and the math score Homework: p. 9 Basic: -6 all, 9,, 43, 47, 53; Etended: 3, 9, 35, 4, 49 Algebra Chapter Page