1.3 Exercises. Vocabulary and Core Concept Check. Dynamic Solutions available at BigIdeasMath.com

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1 1.3 Eercises Dnamic Solutions available at BigIdeasMath.com Vocabular and Core Concept Check 1. COMPLETE THE SENTENCE The linear equation = is written in form.. VOCABULARY A line of best fit has a correlation coefficient of.98. What can ou conclude about the slope of the line? Monitoring Progress and Modeling with Mathematics In Eercises 3 8, use the graph to write an equation of the line and interpret the slope. (See Eample 1.) 3. Tipping. Gasoline Tank Tip (dollars) (1, ) 8 1 Cost of meal (dollars) Fuel (gallons) 8 9 (9, 9) Distance (miles) 9. MODELING WITH MATHEMATICS Two newspapers charge a fee for placing an advertisement in their paper plus a fee based on the number of lines in the advertisement. The table shows the total costs for different length advertisements at the Dail Times. The total cost (in dollars) for an advertisement that is lines long at the Greenville Journal is represented b the equation = +. Which newspaper charges less per line? How man lines must be in an advertisement for the total costs to be the same? (See Eample.) Dail Times 5. Savings Account Balance (dollars) (, 3) 1 Time (weeks) 7. Tping Speed Words tped (1, 55) (3, 165) Time (minutes) 6. Tree Growth 8. Tree height (feet) Volume (cubic feet) 6 6 Age (ears) Swimming Pool (3, 3) (5, 18) Time (hours) Number of lines, Total cost, PROBLEM SOLVING While on vacation in Canada, ou notice that temperatures are reported in degrees Celsius. You know there is a linear relationship between Fahrenheit and Celsius, but ou forget the formula. From science class, ou remember the freezing point of water is C or 3 F, and its boiling point is 1 C or 1 F. a. Write an equation that represents degrees Fahrenheit in terms of degrees Celsius. b. The temperature outside is C. What is this temperature in degrees Fahrenheit? c. Rewrite our equation in part (a) to represent degrees Celsius in terms of degrees Fahrenheit. d. The temperature of the hotel pool water is 83 F. What is this temperature in degrees Celsius? 6 Chapter 1 Linear Functions

2 ERROR ANALYSIS In Eercises 11 and 1, describe and correct the error in interpreting the slope in the contet of the situation. 11. Balance (dollars) Savings Account (, 1) 11 (, 1) 6 Year The slope of the line is 1, so after 7 ears, the balance is $ MODELING WITH MATHEMATICS The data pairs (, ) represent the average annual tuition (in dollars) for public colleges in the United States ears after 5. Use the linear regression feature on a graphing calculator to find an equation of the line of best fit. Estimate the average annual tuition in. Interpret the slope and -intercept in this situation. (See Eample.) (, 11,386), (1, 11,731), (, 11,88) (3, 1,375), (, 1,8), (5, 13,97) 18. MODELING WITH MATHEMATICS The table shows the numbers of tickets sold for a concert when different prices are charged. Write an equation of a line of fit for the data. Does it seem reasonable to use our model to predict the number of tickets sold when the ticket price is $85? Eplain. 1. Income (dollars) 8 6 Earnings (3, 33) (, ) 6 Hours The slope is 3, so the income is $3 per hour. Ticket price (dollars), 17 6 Tickets sold, USING TOOLS In Eercises 19, use the linear regression feature on a graphing calculator to find an equation of the line of best fit for the data. Find and interpret the correlation coefficient In Eercises 13 16, determine whether the data show a linear relationship. If so, write an equation of a line of fit. Estimate when = 15 and eplain its meaning in the contet of the situation. (See Eample 3.) Minutes walking, Calories burned, Months, Hair length (in.), Hours, Batter life (%), Shoe size, Heart rate (bpm), OPEN-ENDED Give two real-life quantities that have (a) a positive correlation, (b) a negative correlation, and (c) approimatel no correlation. Eplain. Section 1.3 Modeling with Linear Functions 7

3 6. HOW DO YOU SEE IT? You secure an interest-free loan to purchase a boat. You agree to make equal monthl paments for the net two ears. The graph shows the amount of mone ou still owe. Loan balance (hundreds of dollars) 3 1 Boat Loan 8 16 Time (months) a. What is the slope of the line? What does the slope represent? b. What is the domain and range of the function? What does each represent? c. How much do ou still owe after making paments for 1 months? 3. MATHEMATICAL CONNECTIONS Which equation has a graph that is a line passing through the point (8, 5) and is perpendicular to the graph of = + 1? A = 1 5 B = + 7 C = 1 7 D = PROBLEM SOLVING You are participating in an orienteering competition. The diagram shows the position of a river that cuts through the woods. You are currentl miles east and 1 mile north of our starting point, the origin. What is the shortest distance ou must travel to reach the river? 8 6 North = 3 + East MAKING AN ARGUMENT A set of data pairs has a correlation coefficient r =.3. Your friend sas that because the correlation coefficient is positive, it is logical to use the line of best fit to make predictions. Is our friend correct? Eplain our reasoning. 8. THOUGHT PROVOKING Points A and B lie on the line = +. Choose coordinates for points A, B, and C where point C is the same distance from point A as it is from point B. Write equations for the lines connecting points A and C and points B and C. 9. ABSTRACT REASONING If and have a positive correlation, and and z have a negative correlation, then what can ou conclude about the correlation between and z? Eplain. 3. ANALYZING RELATIONSHIPS Data from North American countries show a positive correlation between the number of personal computers per capita and the average life epectanc in the countr. a. Does a positive correlation make sense in this situation? Eplain. b. Is it reasonable to conclude that giving residents of a countr personal computers will lengthen their lives? Eplain. Maintaining Mathematical Proficienc Solve the sstem of linear equations in two variables b elimination or substitution. (Skills Review Handbook) = = = 3 = 9 3 = 1 = 1 1 Reviewing what ou learned in previous grades and lessons 36. = = 38. = + = = 1 + = 6 8 Chapter 1 Linear Functions

4 1. Solving Linear Sstems Essential Question How can ou determine the number of solutions of a linear sstem? A linear sstem is consistent when it has at least one solution. A linear sstem is inconsistent when it has no solution. Recognizing Graphs of Linear Sstems Work with a partner. Match each linear sstem with its corresponding graph. Eplain our reasoning. Then classif the sstem as consistent or inconsistent. a. 3 = 3 b. 3 = 3 c. 3 = = 6 + = = 6 A. B. C. Solving Sstems of Linear Equations Work with a partner. Solve each linear sstem b substitution or elimination. Then use the graph of the sstem below to check our solution. a. + = 5 b. + 3 = 1 c. + = = 1 + = 3 + = 1 FINDING AN ENTRY POINT To be proficient in math, ou need to look for entr points to the solution of a problem. Communicate Your Answer 3. How can ou determine the number of solutions of a linear sstem?. Suppose ou were given a sstem of three linear equations in three variables. Eplain how ou would approach solving such a sstem. 5. Appl our strateg in Question to solve the linear sstem. + + z = 1 Equation 1 z = 3 Equation + z = 1 Equation 3 Section 1. Solving Linear Sstems 9

5 1. Lesson Core Vocabular linear equation in three variables, p. 3 sstem of three linear equations, p. 3 solution of a sstem of three linear equations, p. 3 ordered triple, p. 3 Previous sstem of two linear equations What You Will Learn Visualize solutions of sstems of linear equations in three variables. Solve sstems of linear equations in three variables algebraicall. Solve real-life problems. Visualizing Solutions of Sstems A linear equation in three variables,, and z is an equation of the form a + b + cz = d, where a, b, and c are not all zero. The following is an eample of a sstem of three linear equations in three variables z = 3 Equation z = 1 Equation + z = 1 Equation 3 A solution of such a sstem is an ordered triple (,, z) whose coordinates make each equation true. The graph of a linear equation in three variables is a plane in three-dimensional space. The graphs of three such equations that form a sstem are three planes whose intersection determines the number of solutions of the sstem, as shown in the diagrams below. Eactl One Solution The planes intersect in a single point, which is the solution of the sstem. Infinitel Man Solutions The planes intersect in a line. Ever point on the line is a solution of the sstem. The planes could also be the same plane. Ever point in the plane is a solution of the sstem. No Solution There are no points in common with all three planes. 3 Chapter 1 Linear Functions

6 Solving Sstems of Equations Algebraicall The algebraic methods ou used to solve sstems of linear equations in two variables can be etended to solve a sstem of linear equations in three variables. LOOKING FOR STRUCTURE The coefficient of 1 in Equation 3 makes a convenient variable to eliminate. ANOTHER WAY In Step 1, ou could also eliminate to get two equations in and z, or ou could eliminate z to get two equations in and. Core Concept Solving a Three-Variable Sstem Step 1 Rewrite the linear sstem in three variables as a linear sstem in two variables b using the substitution or elimination method. Step Solve the new linear sstem for both of its variables. Step 3 Substitute the values found in Step into one of the original equations and solve for the remaining variable. When ou obtain a false equation, such as = 1, in an of the steps, the sstem has no solution. When ou do not obtain a false equation, but obtain an identit such as =, the sstem has infinitel man solutions. Solving a Three-Variable Sstem (One Solution) Solve the sstem z = 1 Equation 1 SOLUTION 3 + 5z = 7 Equation 6 + z = 3 Equation 3 Step 1 Rewrite the sstem as a linear sstem in two variables z = 1 Add times Equation 3 to 1 + 8z = 6 Equation 1 (to eliminate ) z = 6 New Equation z = z = 9 Add 3 times Equation 3 to Equation (to eliminate ). 16 7z = New Equation Step Solve the new linear sstem for both of its variables z = 6 Add new Equation z = and new Equation. z = 8 z = Solve for z. = 1 Substitute into new Equation 1 or to find. Step 3 Substitute = 1 and z = into an original equation and solve for. 6 + z = 3 Write original Equation 3. 6( 1) + () = 3 Substitute 1 for and for z. = 5 Solve for. The solution is = 1, = 5, and z =, or the ordered triple ( 1, 5, ). Check this solution in each of the original equations. Section 1. Solving Linear Sstems 31

7 Solving a Three-Variable Sstem (No Solution) Solve the sstem. + + z = Equation z = 3 Equation + 3z = 6 Equation 3 SOLUTION Step 1 Rewrite the sstem as a linear sstem in two variables z = 1 Add 5 times Equation z = 3 to Equation. = 7 Because ou obtain a false equation, the original sstem has no solution. ANOTHER WAY Subtracting Equation from Equation 1 gives z =. After substituting for z in each equation, ou can see that each is equivalent to = + 3. Solving a Three-Variable Sstem (Man Solutions) Solve the sstem. + z = 3 Equation 1 SOLUTION z = 3 Equation z = 15 Equation 3 Step 1 Rewrite the sstem as a linear sstem in two variables. + z = 3 z = 3 Add Equation 1 to Equation (to eliminate z). = 6 New Equation z = z = 15 Add Equation to Equation 3 (to eliminate z). 6 6 = 18 New Equation 3 Step Solve the new linear sstem for both of its variables = 18 Add 3 times new Equation 6 6 = 18 to new Equation 3. = Because ou obtain the identit =, the sstem has infinitel man solutions. Step 3 Describe the solutions of the sstem using an ordered triple. One wa to do this is to solve new Equation for to obtain = + 3. Then substitute + 3 for in original Equation 1 to obtain z =. So, an ordered triple of the form (, + 3, ) is a solution of the sstem. 3 Chapter 1 Linear Functions Monitoring Progress Solve the sstem. Check our solution, if possible. Help in English and Spanish at BigIdeasMath.com 1. + z = z = z = z = 7 + z = + z = z = z = + + z = 16. In Eample 3, describe the solutions of the sstem using an ordered triple in terms of.

8 Solving Real-Life Problems Solving a Multi-Step Problem B LAWN B B B A A A B An amphitheater charges $75 for each seat in Section A, $55 for each seat in Section B, and $3 for each lawn seat. There are three times as man seats in Section B as in Section A. The revenue from selling all 3, seats is $87,. How man seats are in each section of the amphitheater? STAGE SOLUTION Step 1 Write a verbal model for the situation. Number of seats in B, = 3 Number of seats in A, Number of seats in A, Number of + seats in B, Number of + lawn seats, z = Total number of seats 75 Number of seats in A, + 55 Number of seats in B, + 3 Number of lawn seats, z = Total revenue Step Write a sstem of equations. = 3 Equation z = 3, Equation z = 87, Equation 3 Step 3 Rewrite the sstem in Step as a linear sstem in two variables b substituting 3 for in Equations and z = 3, Write Equation z = 3, Substitute 3 for. + z = 3, New Equation z = 87, Write Equation (3) + 3z = 87, Substitute 3 for. + 3z = 87, New Equation 3 STUDY TIP When substituting to find values of other variables, choose original or new equations that are easiest to use. Step Solve the new linear sstem for both of its variables. 1 3z = 69, Add 3 times new Equation + 3z = 87, to new Equation 3. 1 = 18, = 15 Solve for. = 5 Substitute into Equation 1 to find. z = 17, Substitute into Equation to find z. The solution is = 15, = 5, and z = 17,, or (15, 5, 17,). So, there are 15 seats in Section A, 5 seats in Section B, and 17, lawn seats. Monitoring Progress Help in English and Spanish at BigIdeasMath.com 5. WHAT IF? On the first da, 1, tickets sold, generating $356, in revenue. The number of seats sold in Sections A and B are the same. How man lawn seats are still available? Section 1. Solving Linear Sstems 33

9 1. Eercises Dnamic Solutions available at BigIdeasMath.com Vocabular and Core Concept Check 1. VOCABULARY The solution of a sstem of three linear equations is epressed as a(n).. WRITING Eplain how ou know when a linear sstem in three variables has infinitel man solutions. Monitoring Progress and Modeling with Mathematics In Eercises 3 8, solve the sstem using the elimination method. (See Eample 1.) 3. + z = z = z = + z = z = 9 + z = z = z = z = z = z = 3 + z = z = z = + z = 7 + 5z = 1 + 3z = z = z = 1. + z = 3 + z = + z = z = z = z = z = z = 1 + z = 5 z = z = MODELING WITH MATHEMATICS Three orders are placed at a pizza shop. Two small pizzas, a liter of soda, and a salad cost $1; one small pizza, a liter of soda, and three salads cost $15; and three small pizzas, a liter of soda, and two salads cost $. How much does each item cost? ERROR ANALYSIS In Eercises 9 and 1, describe and correct the error in the first step of solving the sstem of linear equations. + z = z = z = z = z = z = z = z = 15 + z = MODELING WITH MATHEMATICS Sam s Furniture Store places the following advertisement in the local newspaper. Write a sstem of equations for the three combinations of furniture. What is the price of each piece of furniture? Eplain. SAM S Furniture Store Sofa and love seat In Eercises 11 16, solve the sstem using the elimination method. (See Eamples and 3.) z = z = z = z = + 3z = = 1 Sofa and two chairs Sofa, love seat, and one chair 3 Chapter 1 Linear Functions

10 In Eercises 19 8, solve the sstem of linear equations using the substitution method. (See Eample.) z = 1. 6 z = z = z = z = 11 3 z = z =. + = z = z = + z = 9 + z = z = 1. = + z = 13 + = 6 z = z = z = 6. z = z = z = z = 8 + 3z = z = z = z = 1 + z = 6 z = + z = 6 9. PROBLEM SOLVING The number of left-handed people in the world is one-tenth the number of righthanded people. The percent of right-handed people is nine times the percent of left-handed people and ambidetrous people combined. What percent of people are ambidetrous? 31. WRITING Eplain when it might be more convenient to use the elimination method than the substitution method to solve a linear sstem. Give an eample to support our claim. 3. REPEATED REASONING Using what ou know about solving linear sstems in two and three variables, plan a strateg for how ou would solve a sstem that has four linear equations in four variables. MATHEMATICAL CONNECTIONS In Eercises 33 and 3, write and use a linear sstem to answer the question. 33. The triangle has a perimeter of 65 feet. What are the lengths of sides, m, and n? = 1 m 3 m n = + m What are the measures of angles A, B, and C? A (5A C) A B (A + B) C 3. MODELING WITH MATHEMATICS Use a sstem of linear equations to model the data in the following newspaper article. Solve the sstem to find how man athletes finished in each place. Lawrence High prevailed in Saturda s track meet with the help of individual-event placers earning a combined 68 points. A first-place finish earns 5 points, a secondplace finish earns 3 points, and a third-place finish earns 1 point. Lawrence had a strong second-place showing, with as man second place finishers as first- and third-place finishers combined. 35. OPEN-ENDED Consider the sstem of linear equations below. Choose nonzero values for a, b, and c so the sstem satisfies the given condition. Eplain our reasoning. + + z = a + b + cz = 1 + z = a. The sstem has no solution. b. The sstem has eactl one solution. c. The sstem has infinitel man solutions. 36. MAKING AN ARGUMENT A linear sstem in three variables has no solution. Your friend concludes that it is not possible for two of the three equations to have an points in common. Is our friend correct? Eplain our reasoning. Section 1. Solving Linear Sstems 35

11 37. PROBLEM SOLVING A contractor is hired to build an. HOW DO YOU SEE IT? Determine whether the apartment comple. Each 8-square-foot unit has a bedroom, kitchen, and bathroom. The bedroom will be the same size as the kitchen. The owner orders 98 square feet of tile to completel cover the floors of two kitchens and two bathrooms. Determine how man square feet of carpet is needed for each bedroom. BATHROOM sstem of equations that represents the circles has no solution, one solution, or infinitel man solutions. Eplain our reasoning. a. b. KITCHEN 1. CRITICAL THINKING Find the values of a, b, and c so that the linear sstem shown has ( 1,, 3) as its onl solution. Eplain our reasoning. BEDROOM Total Area: 8 ft + 3z = a + z = b + 3 z = c 38. THOUGHT PROVOKING Does the sstem of linear equations have more than one solution? Justif our answer.. ANALYZING RELATIONSHIPS Determine which arrangement(s) of the integers 5,, and 3 produce a solution of the linear sstem that consist of onl integers. Justif our answer. + + z = + 1 3z = 1 z = 3 + 6z = z = z = PROBLEM SOLVING A florist must make 5 identical bridesmaid bouquets for a wedding. The budget is $16, and each bouquet must have 1 flowers. Roses cost $.5 each, lilies cost $ each, and irises cost $ each. The florist wants twice as man roses as the other two tpes of flowers combined. 3. ABSTRACT REASONING Write a linear sstem to represent the first three pictures below. Use the sstem to determine how man tangerines are required to balance the apple in the fourth picture. Note: The first picture shows that one tangerine and one apple balance one grapefruit. a. Write a sstem of equations to represent this situation, assuming the florist plans to use the maimum budget b. Solve the sstem to find how man of each tpe of flower should be in each bouquet. c. Suppose there is no limitation on the total cost of the bouquets. Does the problem still have eactl one solution? If so, find the solution. If not, give three possible solutions Maintaining Mathematical Proficienc Reviewing what ou learned in previous grades and lessons Simplif. (Skills Review Handbook). ( ) 5. (3m + 1) 6. (z 5) Write a function g described b the given transformation of f() = ( ) (Section 1.) 8. translation units to the left 9. reflection in the -ais 5. translation units up 51. vertical stretch b a factor of 3 Chapter 1 hsnb_alg_pe_1.indd 36 Linear Functions /5/15 9:57 AM

12 What Did You Learn? Core Vocabular line of fit, p. line of best fit, p. 5 correlation coefficient, p. 5 linear equation in three variables, p. 3 sstem of three linear equations, p. 3 solution of a sstem of three linear equations, p. 3 ordered triple, p. 3 Core Concepts Section 1.3 Writing an Equation of a Line, p. Finding a Line of Fit, p. Section 1. Solving a Three-Variable Sstem, p. 31 Solving Real-Life Problems, p. 33 Mathematical Practices 1. Describe how ou can write the equation of the line in Eercise 7 on page 6 using onl one of the labeled points.. How did ou use the information in the newspaper article in Eercise 3 on page 35 to write a sstem of three linear equations? 3. Eplain the strateg ou used to choose the values for a, b, and c in Eercise 35 part (a) on page 35. Secret of the Hanging Baskets A carnival game uses two baskets hanging from springs at different heights. Net to the higher basket is a pile of baseballs. Net to the lower basket is a pile of golf balls. The object of the game is to add the same number of balls to each basket so that the baskets have the same height. But there is a catch ou onl get one chance. What is the secret to winning the game? To eplore the answers to this question and more, go to BigIdeasMath.com. Performance e Task 37

13 1 Chapter Review Dnamic Solutions available at BigIdeasMath.com 1.1 Parent Functions and Transformations (pp. 3 1) Graph g() = ( ) + 1 and its parent function. Then describe the transformation. The function g is a quadratic function. The graph of g is a translation units right and 1 unit up of the graph of the parent quadratic function. f g Graph the function and its parent function. Then describe the transformation. 1. f() = + 3. g() = 1 3. h() = 1. h() = 5. f() = 3 6. g() = 3( + 3) 1. Transformations of Linear and Absolute Value Functions (pp ) Let the graph of g be a translation units to the right followed b a reflection in the -ais of the graph of f() =. Write a rule for g. Step 1 First write a function h that represents the translation of f. h() = f( ) Subtract from the input. = Replace with in f(). Step Then write a function g that represents the reflection of h. g() = h( ) Multipl the input b 1. = Replace with in h(). = ( + ) Factor out 1. = 1 + Product Propert of Absolute Value = + Simplif. The transformed function is g() = +. Write a function g whose graph represents the indicated transformations of the graph of f. Use a graphing calculator to check our answer. 7. f() = ; reflection in the -ais followed b a translation units to the left 8. f() = ; vertical shrink b a factor of 1 followed b a translation units up 9. f() = ; translation 3 units down followed b a reflection in the -ais 38 Chapter 1 Linear Functions

14 1.3 Modeling with Linear Functions (pp. 1 8) The table shows the numbers of ice cream cones sold for different outside temperatures (in degrees Fahrenheit). Do the data show a linear relationship? If so, write an equation of a line of fit and use it to estimate how man ice cream cones are sold when the temperature is 6 F. Temperature, Number of cones, Step 1 Create a scatter plot of the data. The data show a linear relationship. Step Sketch the line that appears to most closel fit the data. One possibilit is shown. Step 3 Choose two points on the line. For the line shown, ou might choose (7, 117) and (9, 17). Step Write an equation of the line. First, find the slope. m = = = 3 = 1.5 Use point-slope form to write an equation. Use ( 1, 1 ) = (7, 117). 1 = m( 1 ) Point-slope form 117 = 1.5( 7) Substitute for m, 1, and = = Distributive Propert Add 117 to each side. Use the equation to estimate the number of ice cream cones sold. = 1.5(6) + 1 Substitute 6 for. = 1 Simplif. Approimatel 1 ice cream cones are sold when the temperature is 6 F. Number of cones Ice Cream Cones Sold (9, 17) (7, 117) 6 8 Temperature ( F) Write an equation of the line. 1. The table shows the total number (in billions) of U.S. movie admissions each ear for ears. Use a graphing calculator to find an equation of the line of best fit for the data. Year, Admissions, You ride our bike and measure how far ou travel. After 1 minutes, ou travel 3.5 miles. After 3 minutes, ou travel 1.5 miles. Write an equation to model our distance. How far can ou ride our bike in 5 minutes? Chapter 1 Chapter Review 39

15 1. Solving Linear Sstems (pp. 9 36) Solve the sstem. + z = 3 Equation 1 + 5z = Equation + z = Equation 3 Step 1 Rewrite the sstem as a linear sstem in two variables. + z = 3 + z = Add Equation 1 to Equation 3 (to eliminate z). 5 + = 1 New Equation z = z = Add 5 times Equation 1 to Equation (to eliminate z). 3 + = 19 New Equation Step Solve the new linear sstem for both of its variables. = Add times new Equation = 19 to new Equation. 3 = 3 = 1 Solve for. = Substitute into new Equation or 3 to find. Step 3 Substitute = 1 and = into an original equation and solve for z. + z = 3 Write original Equation 1. ( 1) + z = 3 Substitute 1 for and for. z = Solve for z. The solution is = 1, =, and z =, or the ordered triple ( 1,, ). Solve the sstem. Check our solution, if possible z = z = z = z = z = z = 11 = z z = 3 + z = z = z = z = z = 1 = z = z = + 5z = z = A school band performs a spring concert for a crowd of 6 people. The revenue for the concert is $315. There are 15 more adults at the concert than students. How man of each tpe of ticket are sold? BAND CONCERT STUDENTS - $3 ADULTS - $7 CHILDREN UNDER 1 - $ Chapter 1 Linear Functions

16 1 Chapter Test Write an equation of the line and interpret the slope and -intercept. 1. Bank Account Balance (dollars) 8 6 (3, 6) (, ) Weeks. Shoe Sales Price of pair of shoes (dollars) 5 3 (, 5) 1 units 1 units 6 8 Percent discount Solve the sstem. Check our solution, if possible z = 5. = 1 z z = z = + + 5z = + 3 z = + 6z = z = 9 9z = 8 Graph the function and its parent function. Then describe the transformation. 6. f() = 1 7. f() = (3) 8. f() = Match the transformation of f() = with its graph. Then write a rule for g. 9. g() = f() g() = 3f() 11. g() = f() 3 A. B. C. 1. A baker sells doughnuts, muffins, and bagels. The baker makes three times as man doughnuts as bagels. The baker earns a total of $15 when all 13 baked items in stock are sold. How man of each item are in stock? Justif our answer. Doughnuts... $1. Muffins... $1.5 Bagels... $ A fountain with a depth of 5 feet is drained and then refilled. The water level (in feet) after t minutes can be modeled b f(t) = 1 t. A second fountain with the same depth is drained and filled twice as quickl as the first fountain. Describe how to transform the graph of f to model the water level in the second fountain after t minutes. Find the depth of each fountain after minutes. Justif our answers. Chapter 1 Chapter Test 1

17 1 Cumulative Assessment 1. Describe the transformation of the graph of f() = represented in each graph. a. g b. g c. g d. 8 8 g 8 e. g f. g. The table shows the tuition costs for a private school between the ears 1 and 13. Years after 1, 1 3 Tuition (dollars), 36,8 37,6 39,88,59 a. Verif that the data show a linear relationship. Then write an equation of a line of fit. b. Interpret the slope and -intercept in this situation. c. Predict the cost of tuition in Your friend claims the line of best fit for the data shown in the scatter plot has a correlation coefficient close to 1. Is our friend correct? Eplain our reasoning. Chapter 1 Linear Functions

18 . Order the following linear sstems from least to greatest according to the number of solutions. A. + z = 7 B z = 5 C. + z = z = 9 + z = z = z = z = z = 5. You make DVDs of three tpes of shows: comed, drama, and realit-based. An episode of a comed lasts 3 minutes, while a drama and a realit-based episode each last 6 minutes. The DVDs can hold 36 minutes of programming. a. You completel fill a DVD with seven episodes and include twice as man episodes of a drama as a comed. Create a sstem of equations that models the situation. b. How man episodes of each tpe of show are on the DVD in part (a)? c. You completel fill a second DVD with onl si episodes. Do the two DVDs have a different number of comedies? dramas? realit-based episodes? Eplain. 6. The graph shows the height of a hang glider over time. Which equation models the situation? A + 5 = 1 B 1 = + 5 C 1 1 = + 5 D 1 + = 5 Height (feet) Hang Gliding Descent Time (seconds) 7. Let f() = and g() = 3. Select the possible transformations (in order) of the graph of f represented b the function g. A reflection in the -ais B reflection in the -ais C vertical translation units down D horizontal translation units right E horizontal shrink b a factor of 1 3 F vertical stretch b a factor of 3 8. Choose the correct equalit or inequalit smbol which completes the statement below about the linear functions f and g. Eplain our reasoning. f() g() f() g() Chapter 1 Cumulative Assessment 3