1.1. Use a Problem Solving Plan. Read a problem and make a plan. Goal p Use a problem solving plan to solve problems. VOCABULARY. Formula.

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1 . Georgia Performance Standard(s) MMPd, MMPa Your Notes Use a Problem Solving Plan Goal p Use a problem solving plan to solve problems. VOCABULARY Formula A PROBLEM SOLVING PLAN Step Read the problem carefull. Identif what ou know and what ou want to find out. Step Decide on the approach to solving the problem. Step Carr out our plan. Tr a new approach if the first one isn t successful. Step 4 Once ou obtain our answer, check to see that it is reasonable. Eample Read a problem and make a plan You have $7 to bu orange juice and bagels at the store. A juice bo costs $. and a bagel costs $.7. If ou bu two juice boes, how man bagels can ou bu? Solution Step What do ou know? You know how much mone ou have, the price of a, and the price of a juice bo. What do ou want to find out? You want to find out the number of ou can bu. Step Use what ou know to write a that represents what ou want to find out. Then write an and solve it. Copright McDougal Littell/Houghton Mifflin Compan. Georgia Notetaking Guide, Mathematics

2 Your Notes Eample Solve a problem and look back Solve the problem in Eample b carring out the plan. Then check our answer. Step Write a verbal model. Then write an equation. Let b be the number of bagels. Price of Number Price of Number Cost juice p of bagel p of (in dollars) (in dollars) boes (in dollars) bagels p p b Step 4 The equation is b. Solve the equation using the strateg guess, check, and revise. Guess an even number that is easil multiplied b. Tr 4. b Write equation. (4) 0 Substitute 4 for b. Simplif; 4 check. Because, tr an even number 4. Tr 6. b Write equation. (6) 0 Substitute 6 for b. Simplif. For ou can bu bagels and juice boes. Each additional bagel ou bu adds to the total cost. Make a table. Bagels Total Cost The total cost is when ou bu bagels and juice boes. The answer in Step is. Georgia Notetaking Guide, Mathematics Copright McDougal Littell/Houghton Mifflin Compan.

3 Your Notes Checkpoint Complete the following eercises.. Suppose in Eample that ou have $ and ou decide to bu three containers of juice. How man bagels can ou bu?. In Eample, the store where ou bought the juice and bagels had an income of $7 from our purchase. The profit the store made from our purchase is $.0. Find the store s epense for the juice and bagels. Homework Copright McDougal Littell/Houghton Mifflin Compan. Georgia Notetaking Guide, Mathematics

4 Name Date LESSON. Practice In Eercises, identif what ou know and what ou need to find out. You do not need to solve the problem.. In science class, ou compare the growths of plants subject to different conditions. Plant A grows inches in the same amount of time plant B grows 7. inches. How man times taller is plant A than plant B?. Your class plans to make a mosaic mural out of -inch b -inch colored tiles. The rectangular mural is 8 feet long and 4 feet tall. How man tiles does our class need to make the mural?. Your baseball team raises $40 to bu new T-shirts and hats. It costs $ for each of the 0 plaers to have a T-shirt and a hat. How much more mone does each plaer have to pa to cover the cost? In Eercises 4 and, state the formula that is needed to solve the problem. You do not need to solve the problem. 4. The temperature is 74 C. What is the temperature in degrees Fahrenheit?. You travel 0 miles to our cousin s house at a rate of 0 miles per hour. When will ou get to our cousin s house? 4 Georgia Notetaking Guide, Mathematics Copright McDougal Littell/Houghton Mifflin Compan.

5 Name Date LESSON. Practice continued 6. Stamp Collection Your stamp collection consists of 0 stamps. Each stamp has either a cancellation mark or no cancellation mark. There are 7 more stamps with cancellation marks than stamps without cancellation marks. Let be the number of stamps without cancellation marks. Which equation correctl models this situation? A. 7 0 B. ( 7) 0 C. ( 7) 0 7. Picnic You are responsible for buing the hamburger rolls for an upcoming picnic. Each bag of rolls costs $.0 and contains 8 rolls. You need to bu a total of 64 rolls. How much mone will it cost for the rolls? 8. Temperature Yesterda s high and low temperatures were 0 F and 4 F, respectivel. What are these temperatures in degrees Celsius? 9. Sandbo A civic group builds a sandbo that is enclosed b -foot wide railroad ties. The group needs to find the area inside the sandbo to find the amount of sand needed. Use the figure and the formula for area to write an epression that represents the area inside the sandbo. ft ft ft ft ft ft Copright McDougal Littell/Houghton Mifflin Compan. Georgia Notetaking Guide, Mathematics

6 . Represent Functions as Rules and Tables Georgia Performance Standard(s) Goal p Represent functions as rules and as tables. MMAd Your Notes VOCABULARY Function Domain Input Range Output Independent variable Dependent variable Eample Identif the domain and range of a function The input-output table shows temperatures over various increments of time. Identif the domain and range of the function. Input (hours) Output ( C) Solution The domain is the set of inputs:. The range is the set of outputs:. 6 Georgia Notetaking Guide, Mathematics Copright McDougal Littell/Houghton Mifflin Compan.

7 Your Notes Eample Make a table for a function The domain of the function is 0,,, and. Make a table for the function, then identif the range of the function. Solution The range of the function is. Eample Write a function rule Write a rule for Input 7 9 the function. Output Solution Let be the input and let be the output. Notice that each output is the corresponding input. So, a rule for the function is. Checkpoint Complete the following eercises.. The domain of the function is, 4,, and 8. Make a table for the function, then identif the range of the function. Homework. Write a rule for the Input 4 function. Identif the Output domain and range. Copright McDougal Littell/Houghton Mifflin Compan. Georgia Notetaking Guide, Mathematics 7

8 Name Date LESSON. Practice Complete the sentence.. The collection of all output values is called the? of a function.. The collection of all input values is called the? of a function. Identif the domain and range of the function.. Input Output 4. Input Output. Input Output Tell whether the pairing is a function. 6. Input Output 7. Input Output 8. Input Output Georgia Notetaking Guide, Mathematics Copright McDougal Littell/Houghton Mifflin Compan.

9 Name Date LESSON. Practice continued Make a table for the function. Identif the range of the function Domain: 0,,, Domain:,,, 7 Domain:, 9, 4, 9. Flower Garden You have a flat of flowers to plant in our garden. a. Write a rule for the number of flowers ou have left in the flat as a function of the number of flowers ou have put in the garden so far. b. Make a table and identif the range of the function.. Centerpieces A florist makes centerpieces for a charit event. She uses 9 flowers in each centerpiece. Write a rule for the total number of flowers used as a function of the number of centerpieces created. 4. Kickboing You join a kickboing class at a local gm. The cost is $ per class plus $ for the initial membership fee. Write a rule for the total cost of the class in dollars as a function of the number of classes ou attend. How much will it cost if ou attend 8 classes? Copright McDougal Littell/Houghton Mifflin Compan. Georgia Notetaking Guide, Mathematics 9

10 . Georgia Performance Standard(s) MMAd Your Notes Represent Functions as Graphs Goal Eample p Represent functions as graphs. Graph a function Graph the function with domain,,, 4, and. Solution Step Make an table. Step Plot a point for each (, ) O Checkpoint Complete the following eercise.. Graph the function } with domain 0,, 6, 9, and O Georgia Notetaking Guide, Mathematics Copright McDougal Littell/Houghton Mifflin Compan.

11 Your Notes Eample Write a function rule for a graph Write a rule for the function represented b the graph. Identif the domain and the range of the function. Solution Step Make a for the graph. 4 O Step Find a outputs. between the inputs and Step Write a that describes the relationship:. The domain of the function is. The range is. Checkpoint Write a rule for the function represented b the graph. Identif the domain and the range of the function. Homework O O Copright McDougal Littell/Houghton Mifflin Compan. Georgia Notetaking Guide, Mathematics

12 Name Date LESSON. Practice Write the ordered pairs that can be formed from the table.. Input Output. Input Output. Input Output Identif the ordered pairs in the graph. Then identif the domain and range O 4 6 O O 4 6 Graph the function Domain: 0,,, Domain: 6,, 4, Domain:,,, O 4 O O Georgia Notetaking Guide, Mathematics Copright McDougal Littell/Houghton Mifflin Compan.

13 Name Date LESSON. Practice continued Match the rule for the function with its graph } A B. 6 4 C O 4 O O 4 D. 6 4 E F O 00 O 4 O 4 6. Hourl Pa The table shows the pa d (in dollars) as a function of the number of hours worked h. Graph the function. Hours worked, h 8 Pa (dollars), d Pa (dollars) d h Hours worked Copright McDougal Littell/Houghton Mifflin Compan. Georgia Notetaking Guide, Mathematics

14 .4 Graph Using Intercepts Georgia Performance Standard(s) MMAb, MMAd Your Notes Goal p Graph a linear equation using intercepts. VOCABULARY -intercept -intercept Eample Find the intercepts of a graph of an equation Find the -intercept and the -intercept of the graph of 8. Solution To find the -intercept, substitute for and solve for. 8 Write original equation. 8 ( ) Substitute for. Solve for. To find the -intercept, substitute for and solve for. 8 Write original equation. 8( ) Substitute for. Solve for. The -intercept is. The -intercept is. 4 Georgia Notetaking Guide, Mathematics Copright McDougal Littell/Houghton Mifflin Compan.

15 Your Notes Checkpoint Find the -intercept and -intercept of the graph of the equation Eample Identif the -intercept and -intercept of the graph. Use a graph to find the intercepts Solution To find the -intercept, look to see where the graph crosses the. The -intercept is. To find the -intercept, look to see where the graph crosses the. The -intercept is. Checkpoint Complete the following eercise.. Identif the -intercept and -intercept of the graph. Copright McDougal Littell/Houghton Mifflin Compan. Georgia Notetaking Guide, Mathematics

16 Eample Use intercepts to graph an equation Graph. 4. Label the points where the line crosses the aes. Solution Step Find the ( ) 4.( ) 4 Step Plot the points that correspond to the intercepts. 7 The -intercept is, so plot and label the point. The -intercept is, so plot and label the point. Step the points b drawing a line through them. CHECK You can check the graph of the equation b using a third point. When,, so the ordered pair is a third solution of the equation. You can see that lies on the graph, so the graph is correct. Checkpoint Complete the following eercise. 4. Graph 7 4. Label the points where the line crosses the aes. Homework 7 6 Georgia Notetaking Guide, Mathematics Copright McDougal Littell/Houghton Mifflin Compan.

17 Name Date LESSON.4 Practice Identif the -intercept and the -intercept of the graph Find the -intercept of the graph of the equation Copright McDougal Littell/Houghton Mifflin Compan. Georgia Notetaking Guide, Mathematics 7

18 Name Date LESSON.4 Practice continued Find the -intercept of the graph of the equation Draw the line that has the given intercepts.. -intercept: 6. -intercept: intercept: -intercept: -intercept: -intercept: Georgia Notetaking Guide, Mathematics Copright McDougal Littell/Houghton Mifflin Compan.

19 Name Date LESSON.4 Practice continued Match the equation with its graph A. B. C. Graph the equation. Label the points where the line crosses the aes Copright McDougal Littell/Houghton Mifflin Compan. Georgia Notetaking Guide, Mathematics 9

20 Name Date LESSON.4 Practice continued 4. Club Membership The computer club at our school is open to juniors and seniors. There are now 4 members in the club. Let be the number of junior members and let be the number of senior members. a. Write an equation for the total number of members in the club. b. Find the intercepts of the equation. Senior members Junior members c. Graph the equation.. Ticket Sales You sold tickets to the school pla. Advance tickets were $6. Tickets sold at the door were $8. Total ticket sales were $480. This situation can be represented b the equation where is the number of advance tickets sold and is the number of tickets sold at the door. a. Find the intercepts of the graph of the equation. Tickets at the door Advance tickets b. Graph the equation. c. If advance tickets were sold, how man tickets were sold at the door? 0 Georgia Notetaking Guide, Mathematics Copright McDougal Littell/Houghton Mifflin Compan.

21 . Find Slope and Rate of Change Georgia Performance Standard(s) MMAg Your Notes Goal VOCABULARY Slope p Find the slope of a line and interpret slope as a rate of change. Rate of change Keep the - and -coordinates in the same order in the numerator and denominator when calculating slope. This will help avoid error. Eample Find a positive slope Find the slope of the line shown. Solution Let (, ) (, ) and (, ) (, ). m } Write formula for slope. () Substitute. Simplif. (, ) (, ) The line is. from left to right. The slope Copright McDougal Littell/Houghton Mifflin Compan. Georgia Notetaking Guide, Mathematics

22 Your Notes Eample Find the slope of the line shown. Solution Let (, ) (, 4) and (, ) (, ). Find a negative slope m } Write formula for slope. (, 4) (, ) 4 Substitute. Simplif. Simplif. The line. from left to right. The slope is Checkpoint Find the slope of the line passing through the points.. (, ) and (, ). (6, ) and (, ) Georgia Notetaking Guide, Mathematics Copright McDougal Littell/Houghton Mifflin Compan.

23 Your Notes Eample Find the slope of a line Find the slope of the line shown. a. (4, ) (, ) b. (4, ) (4, ) Solution a. Let (, ) (, ) and (, ) (4, ). m } 4 The line is. The slope is. b. Let (, ) (4, ) and (, ) (4, ). m } 4 The line is. The slope is. Checkpoint Find the slope of the line passing through the points. Then classif the line b its slope.. (, ) and (, ) 4. (, 7) and (4, 7) Copright McDougal Littell/Houghton Mifflin Compan. Georgia Notetaking Guide, Mathematics

24 Your Notes Eample 4 Find a rate of change Gas Prices The table shows the cost of a gallon of gas for several das. Find the rate of change in price with respect to time. Time (das) Da Da Da Price/gal ($) Rate of change change in cost }} change in time.09 Write formula. Substitute. Simplif. The rate of change in price is per da. Checkpoint Complete the following eercise.. The table shows the temperature of a solution over time. Find the rate of change in temperature with respect to time. Temperature (8F) Time (hours) Homework 4 Georgia Notetaking Guide, Mathematics Copright McDougal Littell/Houghton Mifflin Compan.

25 Name Date LESSON. Practice Tell whether the slope of the line is positive, negative, zero, or undefined Plot the points and draw a line through them. Without calculating, tell whether the slope of the line is positive, negative, zero, or undefined. 7. (, 0) and (, ) 8. (, ) and (, ) 9. (4, ) and (, ) 7 0. (, ) and (, 6). (, ) and (, ). (6, 7) and (7, 6) Copright McDougal Littell/Houghton Mifflin Compan. Georgia Notetaking Guide, Mathematics

26 Name Date LESSON. Practice continued Find the slope of the line that passes through the points.. (0, ) 4. (, ). (, 4) (0, 4) (, 0) (, ) 6. (, 0) (0, ) 7. (0, ) (0, ) 8. (, ) (0, ) 9. (, ) 0. (, ). (.,.) (, ) (, ) (., ) 6 Georgia Notetaking Guide, Mathematics Copright McDougal Littell/Houghton Mifflin Compan.

27 Name Date LESSON. Practice continued Find the slope of the line that passes through the points.. (0, 4) and (, 7). (, ) and (, 0) 4. (, ) and (, ). (4, 8) and (, 6) 6. (4, ) and (, 7) 7. (4, 8) and (6, 0) 8. (, 7) and (, ) 9. (4, ) and (6, ) 0. (, ) and (, 4) Find the value of so that the line passing through the two points has the given slope.. (0, ), (, 7); m }. (, 4), (, ); m }. (4, ), (, ); m 4 Copright McDougal Littell/Houghton Mifflin Compan. Georgia Notetaking Guide, Mathematics 7

28 Name Date LESSON. Practice continued 4. Plant and Flower Sales The table shows the amount of mone (in dollars) spent b a household on plants and flowers for several ears. Describe the rates of change in the number of dollars spent during the time period. Year Amount spent (dollars) Broadwa Shows The graph shows the number of new Broadwa show productions for several ears. a. Describe the rates of change in the number of shows with respect to time. Number of new productions (999, 9) (004, 9) (000, 7) (00, 8) Year (00, 6) (00, 7) b. Determine the time interval(s) during which the number of new shows showed the greatest rate of change. c. Determine the time interval during which the number of new shows showed the least rate of change. 8 Georgia Notetaking Guide, Mathematics Copright McDougal Littell/Houghton Mifflin Compan.

29 .6 Graph Using Slope-Intercept Form Georgia Performance Standard(s) Goal p Graph linear equations using slope-intercept form. MMAb, MMAd Your Notes VOCABULARY Slope-intercept form Parallel Perpendicular Eample Identif the slope and -intercept Identif the slope and -intercept of the line with the given equation. a. b. Solution a. The equation is in the form. So, the slope of the line is, and the -intercept is. b. Rewrite the equation in slope-intercept form b solving for. Write original equation. Add to each side. The line has a slope of and a -intercept of. Copright McDougal Littell/Houghton Mifflin Compan. Georgia Notetaking Guide, Mathematics 9

30 Your Notes Checkpoint Identif the slope and -intercept of the line with the given equation Eample Graph an equation using slope-intercept form Graph the equation 4. Solution Step Rewrite the equation in slope-intercept form. Step the slope and the -intercept. m b Step the point that corresponds to the -intercept, ( ). Step 4 Use the slope to locate a second point on the line. Draw a line through the two points. Checkpoint Complete the following eercise.. Graph the equation }. 0 Georgia Notetaking Guide, Mathematics Copright McDougal Littell/Houghton Mifflin Compan.

31 Your Notes Eample Identif parallel and perpendicular lines Determine which of the lines are parallel or perpendicular: line a through (4, ) and (, 4), line b through (, 4) and (, ), line c through (, 4) and (6, ), and line d through (, ) and (4, ). Solution Find the slope of each line. Line a: Line b: Line c: () (4) 4 () (4) () Line d: () () Lines and have the same slope, so the are. Lines and have slopes that are negative reciprocals, so the are. Checkpoint Complete the following eercise. Homework 4. Determine which of the lines are parallel or perpendicular. Line a: through (, ) and (, ) Line b: through (4, ) and (, 4) Line c: through (, ) and (, 0) Line d: through (8, 6) and (, 8) Copright McDougal Littell/Houghton Mifflin Compan. Georgia Notetaking Guide, Mathematics

32 Name Date LESSON.6 Practice Identif the slope and -intercept of the line whose graph is shown Identif the slope and -intercept of the line with the given equation }. } Georgia Notetaking Guide, Mathematics Copright McDougal Littell/Houghton Mifflin Compan.

33 Name Date LESSON.6 Practice continued Graph the equation } 0. } 4. } } 4. } 4 4. } Copright McDougal Littell/Houghton Mifflin Compan. Georgia Notetaking Guide, Mathematics

34 Name Date LESSON.6 Practice continued Tell whether the graphs of the two equations are parallel lines, perpendicular lines, or neither.., 4 6., 6 7. Landscape Architect A landscape architect charges $00 for an initial consultation and then charges $8 an hour to design the landscaping for an area. The total cost C (in dollars) is given b the equation C 00 8t where t is the time (in hours) the architect works on the design. a. Graph the equation. b. Suppose the architect raises the fee for the initial consultation to $ so that the total cost of a design that takes t hours to create is given b the equation C 8t. Graph the equation on the same coordinate plane as the equation in part (a). Cost (dollars) C Time (hours) t c. How much more does it cost for a design if it takes the architect 6 hours to create the design? 8. Drum Lessons You are taking drum lessons at a studio. Last ear, the studio charged $0 per lesson. This ear, the studio raised its rates and charges $ per lesson. The total fee f (in dollars) for taking lessons last ear is given b the equation f 0l where l is the number of lessons ou took. The total fee this ear is given b the equation f l. Graph the equations in the same coordinate plane. Use the graphs to find the difference between the fees a person could be charged for taking 48 lessons. Fee (dollars) f Number of lessons 4 Georgia Notetaking Guide, Mathematics Copright McDougal Littell/Houghton Mifflin Compan.

35 .7 Graph Linear Functions Georgia Performance Standard(s) MMAa, MMAb, MMAc Goal p Use function notation. VOCABULARY Function notation Your Notes Famil of functions Parent linear function Eample Find a function value Evaluate f() when. Solution f() Write original function. f( ) ( ) Substitute for. Simplif. When, f(). Eample Find an -value For the function f(), find the value of so that f() 0. Solution f() Write original function. Substitute for f(). Solve for. When, f() 0. Copright McDougal Littell/Houghton Mifflin Compan. Georgia Notetaking Guide, Mathematics

36 Your Notes Checkpoint Complete the following eercises.. Evaluate f() 7 when.. For f() 6 6, find the value of so that f() 4. Eample Compare graphs with the graph of f() Graph the function. Compare the graph with the graph of f(). a. p() 4 b. r() Solution a. Because the graphs of p and f have the same slope, m, the lines are. Also, the -intercept of the graph of p is less than the -intercept of the graph of f. The graph of p is a from the graph of f. b. Because the graphs of r and f have the same slope, m, the lines are. Also, the -intercept of the graph of r is more than the -intercept of the graph of f. The graph of r is a from the graph of f. 6 Georgia Notetaking Guide, Mathematics Copright McDougal Littell/Houghton Mifflin Compan.

37 Your Notes Eample 4 Compare graphs with the graph of f() Graph the function. Compare the graph with the graph of f(). a. q() 4 b. h() } 6 Solution a. The graph of q is f() which means each value of f is multiplied b. The graph of q is a vertical of the graph of f using a scale factor of. b. The graph of h is f() which means each value of f is multiplied b. The graph of h is a vertical of the graph of f using a scale factor of. Checkpoint Graph the function. Compare the graph with the graph of f().. d() 6 4. r() } 7 Copright McDougal Littell/Houghton Mifflin Compan. Georgia Notetaking Guide, Mathematics 7

38 Your Notes Eample Compare graphs Graph the functions. Compare the graphs. a. g(), b. p(), h() q() Solution a. The graph of h is a b. The graph of q is a reflection of the graph reflection of the graph of g in the. of p in the. Checkpoint Complete the following eercise.. Graph v() } and w() }. Compare the graphs. Homework 8 Georgia Notetaking Guide, Mathematics Copright McDougal Littell/Houghton Mifflin Compan.

39 Name Date LESSON.7 Practice Evaluate the function when, 0, and.. f() 0. g() 7. p() 4 4. p() 9. d() 6. f() 4 7. h() 8. m() 8 9. f(). 0. s().. d() }. h() } 4 Find the value of so that the function has the given value.. h() ; 9 4. m() ; 7. p() ; 6. f() 4 ; 9 7. g() 8; 8. h() 6 ; 7 9. m() 8 0; 6 0. p() 8 ; 6. d() ;. f() 8; 0. g() 0; 0 4. h() 8 0; 6 Copright McDougal Littell/Houghton Mifflin Compan. Georgia Notetaking Guide, Mathematics 9

40 Name Date LESSON.7 Practice continued Compare the graph of g() to the graph of f().. g 6. f 7. f f g 6 g 8. g 9. f 6 f g 6 0. g f 6 40 Georgia Notetaking Guide, Mathematics Copright McDougal Littell/Houghton Mifflin Compan.

41 Name Date LESSON.7 Practice continued Graph the function. Compare the graph of g() to the graph of f().. g() 4. g(). g() } Graph the functions. Compare the graphs. 4. g(), h(). p(), q() Copright McDougal Littell/Houghton Mifflin Compan. Georgia Notetaking Guide, Mathematics 4

42 Name Date LESSON.7 Practice continued 6. Savings The value of a savings account (in dollars) from 990 to 006 can be modeled b the function f() 06 8 where is the number of ears since 990. a. Graph the function and identif its domain and range. Value of account (dollars) f() Years since 990 b. Find the value of f() when. Eplain what the solution means in this situation. c. Find the value of so that f() 000. Eplain what the solution means in this situation. 7. Newspapers The average monthl cost (in dollars) of a subscription to a newspaper from 000 to 006 can be modeled b the function f().6. where is the number of ears since 000. a. Graph the function and identif its domain and range. Cost (dollars) f() Years since 000 b. Find the value of so that f() 8. Eplain what the solution means in this situation. 4 Georgia Notetaking Guide, Mathematics Copright McDougal Littell/Houghton Mifflin Compan.

43 .8 Predict with Linear Models Georgia Performance Standard(s) MMAd Your Notes Goal p Make predictions using best-fitting lines. VOCABULARY Best-fitting line Linear interpolation Linear etrapolation Zero of a function Copright McDougal Littell/Houghton Mifflin Compan. Georgia Notetaking Guide, Mathematics 4

44 Your Notes Eample Interpolate using an equation Salaries The table shows a compan's annual salar ependiture (in thousands of dollars) from 000 to 004. Year Annual Salar Ependiture (in thousands of dollars) a. Make a scatter plot of the data. b. Find an equation that models the annual salar ependiture (in thousands of dollars) as a function of the number of ears since 000. c. Approimate the annual salar ependiture in 00. Solution a. Enter the data into lists on a graphing calculator. Make a scatter plot, letting the number of ears since 000 be the (0,,, 4) and the annual salar ependiture be the. b. Use a calculator to find the best-fitting line. The equation of the best-fitting line is. c. Graph the best-fitting line. Use the trace feature and the arrow kes to find the value of the equation when. The annual salar ependiture in 00 was thousand dollars. Y=94X+ X= Y= Georgia Notetaking Guide, Mathematics Copright McDougal Littell/Houghton Mifflin Compan.

45 Your Notes Eample Etrapolate using an equation Salaries Look back at Eample. a. Use the equation from Eample to approimate the annual total salar ependiture in 00 and 006. b. In 00, the annual total salar ependiture was actuall 80 thousand dollars. In 006, the annual total salar ependiture was actuall 9 thousand dollars. Describe the accurac of the etrapolations made in part (a). Solution a. Evaluate the equation of the best-fitting line from Eample for and. The model predicts the average annual salar ependiture as thousand dollars in 00 and thousand dollars in 006. b. The differences between the predicted annual salar ependiture and the actual annual salar ependiture in 00 and 006 are thousand dollars and thousand dollars, respectivel. The difference in actual and predicted annual salar ependitures increased from 00 to 006. So, the equation of the best-fitting line gives a less accurate prediction for ears farther from the given data. Checkpoint Complete the following eercise.. Population The table shows the population of a town from 00 to 006. Year Population Find an equation that models the population as a function of the number of ears since 00. Approimate the population in 00, 007, and 008. Copright McDougal Littell/Houghton Mifflin Compan. Georgia Notetaking Guide, Mathematics 4

46 Your Notes Eample Find the zero of a function Public Transit The percentage of people in the U.S. that use public transit to commute to work can be modeled b the function where is the number of ears since 98. Find the zero of the function to the nearest whole number. Eplain what the zero means in this situation. Solution Substitute for in the model and solve for Write the equation Substitute for. Solve for. The zero of the function is about. According to the model, there will be no people who use public transit to commute to work ears after, or in. Checkpoint Complete the following eercise.. Profit The profit p of a compan can be modeled b p 00 t where t is the number of ears since 000. Find the zero of the function. Eplain what the zero means in this situation. Homework 46 Georgia Notetaking Guide, Mathematics Copright McDougal Littell/Houghton Mifflin Compan.

47 Name Date LESSON.8 Practice Create a scatter plot of the data Find the equation of the best-fitting line. Approimate the value of for Copright McDougal Littell/Houghton Mifflin Compan. Georgia Notetaking Guide, Mathematics 47

48 Name Date LESSON.8 Practice continued Determine whether the -value is a zero of the function. 9. f(), 0. f() 8, 4. f() 4, 8. f() 6,. f() 7, 4. f() }, 6. f() } 4 8, } 6. f() 6 } 4, } 7. f() 6 0, f() 9, f(), f()., 0.4. f() },. f() 4 } 4, } 6. f().6 4, Georgia Notetaking Guide, Mathematics Copright McDougal Littell/Houghton Mifflin Compan.

49 Name Date LESSON.8 Practice continued Find the zero of the function. 4. f() 0. f() 6. f() 8 7. f() 8. f() 9 9. f() 6 0. f() 8 4. f() 0 0. f() }. f() } f() 7. f() } Copright McDougal Littell/Houghton Mifflin Compan. Georgia Notetaking Guide, Mathematics 49

50 Name Date LESSON.8 Practice continued 6. Movies The table shows the number of movies for several ears watched b a critic. Year Number of movies a. Make a scatter plot of the data. Let represent the number of ears since 99 and let represent the number of movies. b. Find an equation that models the number of movies as a function of the number of ears since 99. Number of movies Movies Years since Dair The table shows the cost of a dair product from 00 to 006. Year Cost (dollars) a. Make a scatter plot of the data. Let represent the number of ears since 00 and let represent the cost of the dair product. b. Find an equation that models the cost (in dollars) of the dair product as a function of the number of ears since 00. Cost (dollars) Dair Years since 00 c. Approimate the cost of the dair product in Georgia Notetaking Guide, Mathematics Copright McDougal Littell/Houghton Mifflin Compan.

51 .9 Graph Absolute Value Functions Georgia Performance Standard(s) MMAa, MMAb, MMAc Your Notes Goal p Graph absolute value functions. VOCABULARY Absolute value Absolute value function GRAPH OF PARENT FUNCTION FOR ABSOLUTE VALUE FUNCTIONS f () u u COMPARING GRAPHS OF ABSOLUTE VALUE FUNCTIONS WITH THE GRAPH OF f() g() h The graph of g is a shift of the graph of f(). The shift is h units if h > 0 and h units if h < 0. The graph of h() h is a in the -ais of the graph of g. g() k The graph of g is a shift of the graph of f(). The shift is k units if k > 0 and k units if k < 0. g() a If a >, the graph of g is a vertical of the graph of f(). If 0 < a <, the graph of g is a vertical of the graph of f(). The graph of h() a is a in the -ais of the graph of g. Copright McDougal Littell/Houghton Mifflin Compan. Georgia Notetaking Guide, Mathematics

52 Your Notes Eample Graph g() h and g() k Graph (a) g() and (b) g(). Compare the graph with the graph of f(). Make a table of values. Graph the function. Compare the graphs of g and f. a. b. 0 g() The graph of g() is a of the graph of f(). 0 g() The graph of g() is a of the graph of f(). f f Checkpoint Graph the function. Compare the graph with the graph of f().. g(). g() 7 f f Georgia Notetaking Guide, Mathematics Copright McDougal Littell/Houghton Mifflin Compan.

53 Your Notes Eample Graph g() a Graph (a) g() and (b) g() 0.6. Compare the graph with the graph of f(). Make a table of values. Graph the function. Compare the graphs of g and f. a. 0 g() The graph of g() opens and is a of the graph of f(). b. 0 g() The graph of g() 0.6 opens and is a of the graph of f(). f f Checkpoint Graph the function. Compare the graph with the graph of f().. g(). 4. g() f f Homework Copright McDougal Littell/Houghton Mifflin Compan. Georgia Notetaking Guide, Mathematics

54 Name Date LESSON.9 Practice Match the function with its graph.. f() 4. f() } 4. f() 4 A. B. C. Match the function with its graph. 4. f(). f() 6. f() A. B. C. 4 Georgia Notetaking Guide, Mathematics Copright McDougal Littell/Houghton Mifflin Compan.

55 Name Date LESSON.9 Practice continued Graph the function. Compare the graph with the graph of f (). 7. g() 8. g() 9. g() 4 0. g(). g() } 0. g() Copright McDougal Littell/Houghton Mifflin Compan. Georgia Notetaking Guide, Mathematics

56 Words to Review Give an eample of the vocabular word. Formula Function Domain, Input Range, Output Independent variable Dependent variable -intercept -intercept Slope Rate of change 6 Georgia Notetaking Guide, Mathematics Copright McDougal Littell/Houghton Mifflin Compan.

57 Slope-intercept form Parallel Perpendicular Function notation Famil of functions Parent linear function Best-fitting line Linear interpolation Linear etrapolation Zero of a function Absolute value Absolute value function Copright McDougal Littell/Houghton Mifflin Compan. Georgia Notetaking Guide, Mathematics 7