Chapter 4. Chapter 4 Opener. Section 4.1. Big Ideas Math Blue Worked-Out Solutions. x 2. Try It Yourself (p. 147) x 0 1. y ( ) x 2

Transcription

1 Chapter Chapter Opener Tr It Yourself (p. 7). As the input decreases b, the output increases b.. Input As the input increases b, the output increases b.. As the input decreases b, the output decreases b.. Section.. Activit (pp. ). a. + = + = = = ( ) = = The equation in function form is =. Domain =,,,, = is not in the domain because the output becomes negative, and ou cannot sell a negative amount of child tickets. = is not in the domain because ou cannot sell half of an adult ticket. c. =,,,, d. Input, Output Output, The ordered pairs are (,, ) (,, ) (,, ) (,, ) and (, ).. a. ( ) + = ( ) ( ) + = () + = ( ) + = The domain is,,,, and. The range is, 7,,, and. = () = ( ) = () = ( ) ( ) = The domain is,,,, and. The range is,,,, and. c. 7 7 The domain is,,, 7, and. The range is, 7,,, and. d. 7 + = 7 The domain is,,,, and. The range is,,,, and 7.. You can find the domain of a function b determining the input values of the function. You can find the range of a function b determining the output values of the function. Copright Big Ideas Learning, LLC 7

2 Chapter. a. Woman s foot: = + 7; Man s foot: = + 7. b c. Woman s foot: Domain Domain Domain Shoe size, Length of foot, Shoe size, 7 Length of foot, Shoe size, Length of foot, 7 Domain Domain. On Your Own (pp. ). Ordered pairs: (,, ) (,, ) (,, ) (, ) The domain is,,, and. The range is.. Ordered pairs: (, ), (, ), (, ), (, ), and (, ).. Shoe size, Length of foot, Shoe size, Length of foot, The domain is,,,, and. The range is,, and. ( ) = ( ) = Domain Shoe size, Length of foot, () = ( ) = The domain is,,, and. The range is,,, and. Domain Shoe size, Length of foot,. + = = Man s foot: = = Domain Shoe size, Domain Length of foot, Shoe size, = = The domain is,,, and. The range is,,, and. Domain Domain Length of foot, Shoe size, Length of foot, Shoe size,. a. Zero das after December 7 is December 7. One da after December 7 is December. So, the domain,,,, and represents December 7,,,, and. The range is.,.,.,., and.. These amounts are increasing, so the moon is more visible each da. December, corresponds to the input =. When =, =.. So,., or % of the moon was visible on December,. Length of foot, 7 Copright Big Ideas Learning, LLC

3 Chapter. Eercises (pp. ) Vocabular and Concept Check. no; The equation = is not in function form because it is not solved for.. ( ) = ( ) =. The first statement is different because it asks for the range of the function and the other three ask for the domain. The domain is,, and. The range is 7,, and. Practice and Problem Solving. a. + = = = The domain is,,, and. The range is,,, and. c. = is not in the domain of the function because it would make negative, and it is not possible to bu a negative number of headbands.. Ordered pairs: (, ), (, ), (, ), (, ) The domain is,,, and. The range is,,, and.. Ordered pairs: (,, ) (,, ) (,, ) (,, ) (, ) The domain is,,,, and. The range is,, and.. Ordered pairs: (, ), (, ), (, ), (, ) The domain is,,, and. The range is,,, and. 7. The domain and range are switched. The domain should be the set of inputs represented b the -values. The range should be the set of outputs represented b the,,,,,, -values. The ordered pairs are ( ) ( ) ( ) and (, ). So, the domain is,,, and. The range is,,, and.. The domain is,,, and. The range is,,, and.. ( ) + = ( ) + = () + = ( ) + = The domain is,,, and. The range is,,, and.. The domain is,,, and. The range is,,, and. The domain is,,, and. The range is.,,., and.. a. The domain is,, and. The range is., 7., and.. The domain represents the round of the competition. The range is increasing, so the vaulter s scores are increasing with each round. c. mean = =. = 7. The mean score of the vaulter is 7... a. Words: Amount manatee eats is % of its bod weight. Variables: Let be the amount that the manatee eats and be the manatee s bod weight. Equation: =. An equation in function form is =.. () = ( ) =.( ) + =..( ) + =.() + =..( ) + = Input,. Output,.( ).( ).( ).( ) 7 7.( 7 ).( ) Copright Big Ideas Learning, LLC

4 Chapter c. For the function, the domain is the set of positive numbers that are possible weights of manatees. An approimation would be the positive numbers up to. The range would be the positive numbers up to about. For the input-output table shown, the domain is the -values and the range is the -values. d. The manatees weigh a total of = pounds. In a da, these manatees would eat =. = pounds of food. ( ) In a week, the would eat = 7 = 7 pounds of food. ( ). a. The distance between and on a number line is. The distance between and on a number line is. So, the domain is an number and the range is an number greater than or equal to. The domain is an number. The range is the opposite of the range of =. So, the range is an number less than or equal to. c. The domain is an number. The range is the range of = minus. So, the range is an number greater than or equal to. d. The domain is an number. The range is the range of = plus. So, the range is an number less than or equal to. Fair Game Review. + (, ) ( ) + (, ) ( ) + (, ) O = = = ( ) = = (, ) ( ) (, ) () = = + = + = O ( ), (, ) ( ) () (, ) (, ) Copright Big Ideas Learning, LLC

5 Chapter. 7. D; The number of people in a group must be greater than or equal to. So, an inequalit is. Section. (, ) 7 ( ) (, ) 7 () (, ) O. Activit (pp. ). a. Let be the total hotel cost and let be the number of rooms. Total Cost per room Number = cost per night of rooms A function for the total hotel cost is = + =. Total hotel cost 7 ( )( ) Hotel Reservations Number of rooms Domain:,,,,,, :,,,,,, The domain is discrete because it consists of onl the numbers,,,,,, and. Let be the total weight and let be the weight per piece. Total Pieces of Weight = weight luggage per piece A function for the total weight of the luggage is =. Domain: and : and The domain is continuous because it consists of all numbers from to on the number line.. The domain of a function is discrete if its set of input values consists of onl certain numbers in an interval. The domain of a function is continuous if its set of input values consists of all numbers in an interval. Sample answer: The total ticket sales for various numbers of tickets represents a function with a discrete domain. The total distance traveled for various times t represents a function with a continuous domain.. On Your Own (pp. 7). Total weight of luggage Input, d 7 7 Luggage Weight Pounds per piece d Output, m Ordered Pair d, m ( ) ( ) (, ) () (, ) ( ) (, ) () (, ) ( ) (, ) ( ) (, ) Copright Big Ideas Learning, LLC Mone left (dollars) m (, ) (, ) (, ) (, ) (, ) (, ) d Number of DVDs Because ou cannot bu part of a DVD, the graph consists of individual points. So, the domain is discrete.

6 Chapter. Let g be the number of gallons remaining and let m be the number of minutes. Gallons remaining Draining rate Number = of minutes ( gal min) The function is g =. m. Gallons remaining Input, m.m Because parts of minutes are possible, m can be an value greater than or equal to. So, the domain is continuous.. Part of a stor of a building is not possible, so the data is discrete.. Eercises (pp. ) Output, g Ordered m, g Pair ( ).( ) (, ).( ) (, ).( ) (, ).( ) (, ).() (, ) g (, ) (, ) (, ) (, ) (, ) m Minutes Vocabular and Concept Check. A discrete domain is a set of input values that consists of onl certain numbers in an interval. A continuous domain is a set of input values that consists of all numbers in an interval.. If a graph consists of individual points, then the domain is discrete. If the graph is a line, then the domain is continuous. Practice and Problem Solving. The domain is and. The range is and. The domain is continuous because it consists of all numbers from to on the number line Marbles (, ) (, ) (, ) Bags Because ou cannot have part of a bag, the graph consists of individual points. So, the domain is discrete. Height (feet) (, ) (, ) (, ) Years Because parts of ears are possible, can be an value greater than or equal to and the graph is a line. So, the domain is continuous. Volume (in. ) (, ) 7 Width (in.) Because parts of measurements are possible, can be an value greater than and the graph is a line. So, the domain is continuous. Cost (dollars) (, ) (,.) (, ) (,.) (, ) Hats Because ou cannot have part of a hat, the graph consists of individual points. So, the domain is discrete.. The graph consists of individual points. So, the domain is discrete, not continuous.. The domain is,,,,,, and. The range is,,,,,, and. The domain is discrete because it consists of onl the numbers,,,,,, and. Copright Big Ideas Learning, LLC

7 Chapter. Because ou cannot bu part of a ball of arn, the graph consists of individual points. So, the domain is discrete.. Because a part of a measurement is possible and a part of a shirt is not possible, the function whose input is length has a continuous domain.. Mone left (dollars) Feet Input, b.b Output, m m Ordered bm, Pair ( ).( ) (, ).(). (,. ).( ) (, ).(). (,. ) (, ) (,.) (, ) (,.) b Balls of arn Input,. Output, Ordered, Pair ( ).( ) (, ).(). (,. ).( ). (,. ).(). (,. ).( ). (,. ) 7 Meters Because ou can have part of a measurement, can be an value greater than or equal to. So, the domain is continuous.. A = bh = () h = h The function is A = h. Area (in. ) Because ou can have part of a measurement, h can be an value greater than or equal to. So, the domain is continuous.. a Input, h h Output, A A From the table, is an input value so it is in the domain. From the table, is an output value, so it is in the range.. a. Words: Number of -inch frames times length of frame plus number of -inch frames times length of frame equals length of shelf Variables: Let be the number of -inch frames and let be the number of -inch frames. Function: + = + = = = A function is =. Ordered h, A Pair ( ) ( ) (, ) () (, ) ( ) (, ) () (, ) ( ) (, ) 7 h Height (in.) Input, Output, Ordered, Pair ( ) ( ) (, ) ( ) (, ) () (, ) ( ) (, ) Copright Big Ideas Learning, LLC

8 Chapter -inch frames Input, c. Because ou cannot have part of a frame, the graph consists of individual points. So, the domain is discrete. Fair Game Review. Two points on the line are (, ) and (, ). rise slope = = = run The slope is. 7. Two points on the line are (, ) and (, ). rise slope = = = run The slope is.. Two points on the line are (, ) and (, ). rise slope = = run The slope is.. C; The graph crosses the -ais at =. So, the -intercept is. Stud Help (p. ) Available at BigIdeasMath.com. Quiz.. (p. ) Output, Ordered,. Ordered pairs: (,, ) (,, ) (,, ) (, ) Pair ( ) ( ) (, ) ( ) (, ) ( ) (, ) ( ) (, ) 7 -inch frames The domain is,,, and. The range is,,, and.. Ordered pairs: (, ), (, ), (, ), (, ), (, ) The domain is,,,, and. The range is,, and.. Ordered pairs: (, ), (, ), (, ), (, ). The domain is,,, and. The range is. The domain is,,, and. The range is,,, and.. + = = ( ) = () = ( ) = () = ( ) + = ( ) () + = ( ) + = + = The domain is,,, and. The range is,,, and. Cost (dollars) Rulers Because ou cannot have part of a ruler, the graph consists of individual points. So, the domain is discrete. Miles remaining Gallons Because part of a gallon is possible, can be an value greater than or equal to and the graph is a line. So, the domain is continuous. Copright Big Ideas Learning, LLC

9 Chapter... Height Because part of a minute is possible, can be an value greater than or equal to and the graph is a line. So, the domain is continuous. Athletes Because ou cannot have part of a team, the graph consists of individual points. So, the domain is discrete. Mone Left Because ou cannot rent part of a video game, the graph consists of individual points. So, the domain is discrete.. a. Words: Water weight is % of bod weight. Variables: Let be the water weight and let be the bod weight. Equation: =. An equation in function form is =.. Minutes Rela teams Input, r r Output, m m Ordered r, m Pair ( ) ( ) (, ) () 7 (, 7 ) ( ) (, ) () (, ) ( ) (, ) r Video Games Rented Input,. Output,.( ).( ) 7.( ).( ) Section.. Activit (pp. ). a. c. 7 rise slope = = =. run Because the graph crosses the -ais at (, ), the -intercept is. So, the linear function is =. +. rise slope = = run Because the graph crosses the -ais at (, ), the -intercept is. So, the linear function is rise slope = = = run O = +. Because the graph crosses the -ais at (, ), the -intercept is. So, the linear function is = +. Copright Big Ideas Learning, LLC

10 Chapter d. rise slope = = run Because the graph crosses the -ais at (, ), the -intercept is. So, the linear function is =.. a. The table represents the circumference of the circle. A linear function is = π, where is the radius and is the circumference. π π π π π The table represents the perimeter of the rectangle. A linear function is = + = +, where is the width and is the perimeter. c. The table represents the area of the trapezoid. A linear function is = ( + ) = +, where is the length of the top base and is the area. d. The table represents the surface area of the prism. Surface area = ( ) + ( ) + ( ) = + + = + A linear function is = +, where is the width and is the surface area.. Sample answer: A linear function helps ou to see the relationship between and. The slope shows the rate at which is changing for each increase of in.. Sample answer: In Activit, to find the linear functions, first find the slope; then find the -intercept. In Activit, to find the linear functions, use a familiar geometric formula.. On Your Own (pp. ) rise. slope = = run. 7,, the Because the line crosses the -ais at ( ) -intercept is. So, the linear function is O slope = = =. Because the line crosses the -ais at (, ), the -intercept is. So, the linear function is = +, or =. Copright Big Ideas Learning, LLC

11 Chapter. Calories Burned a. Time can represent an value greater than or equal to, so the domain is continuous. The slope is = and the -intercept is. So, the linear function is =. = =. = 7 c. ( ) You burn 7 calories in. hours of rock climbing.. Eercises (pp. 7) Vocabular and Concept Check. You can represent a function with words, an equation, a table, and a graph.. no; The function is not linear because its graph is not a line. Practice and Problem Solving. The table represents the circumference of the circle. A linear function is = π, where is the diameter and is the circumference. π π π π π. The table represents the area of the triangle. A linear function is = =, where is the base and is the area. 7 (, ) (, 7) (, ) (, ) Hours Rock Climbing rise slope = = = run Because the line crosses the -ais at (, ), the -intercept is. So, the linear function is =. rise slope = = = run Because the line crosses the -ais at (, ), the -intercept is. So, the linear function is = +, or =. O rise slope = = = run Because the line crosses the -ais at (, ), the -intercept is. So, the linear function is = + or =. rise slope = = run Because the line crosses the -ais at (, ), the -intercept is. So, the linear function is O = +, or =.. rise slope = = = run Because the line crosses the -ais at (, ), the -intercept is. So, the linear function is = +. Copright Big Ideas Learning, LLC 7

12 Chapter.. a. O rise slope = = run Because the line crosses the -ais at (, ), the -intercept is. So, the linear function is Cost (dollars) (, ) (, ) (, ) (, ) Number of Movies = +. Because ou cannot rent part of a movie, the graph consists of individual points. So, the domain is discrete. rise slope = = = run Because the line crosses the -ais at (, ), the -intercept is. So, the linear function is = +, or =. c. = = () = It costs $ to rent three movies.. a.. (,.).. (,.). (,.) Weight (lb) The points lie on a line, and as weight increases, the height decreases. rise. slope = = =. run Height (in.) Because the line crosses the -ais at (, ), the -intercept is. So, the linear function is =. +. c.. a.. a. =. + =.(.) + =. + =.7 For a bike that weighs. pounds, the height of a bunn hop is.7 inches. rise slope = = = run Because the graph crosses the -ais at (, ), the -intercept is. So, the linear function is = +. c. = + = () + = + = 7 The annual salar of a person after ears of education beond high school is $7,. Annual salar (thousands of dollars) Heat Inde ( F) 7 Temperature ( F, ) t Heat Inde ( ) H rise slope = = = run Etending the graph, the line crosses the H-ais at,. The H-intercept is. ( ) (, ) (, ) (, ) (, ) (, ) Years of education So, the linear function is H = t. F, H + = + = 7 + = + = Temperature ( F) t Copright Big Ideas Learning, LLC

13 Chapter c. H = t = ( ) = = The Heat Inde is F when the temperature is F. Fair Game Review.. I = Prt ()() r = = r. = r The annual simple interest rate is., or %. I = Prt = ( r) = r. = r The annual simple interest rate is., or %. 7. B; Words: Total cost equals cost of seed packets times number of seed packets plus cost of gardening gloves. Variables: Let be the total cost and let be the number of seed packets. Equation: =. +. An equation is =. +.. Section.. Activit (pp. ). a. P = + = + = P P () = ( ) = () = P ( ) = ( ) = 7 The pattern appears to be linear.. a. A = = A The pattern appears to be nonlinear. The graph appears to be linear. A () = ( ) = () = A ( ) = () = 7 Height (feet) Height (feet) h 7 t Time (seconds) h 7 t Time (seconds) The graph appears to be nonlinear. The bowling ball has an increasing speed because the height decrease is greater with each second.. A pattern in real life is linear if the rate of change is constant. A pattern in real life is nonlinear if the rate of change is not constant. Sample answer: A real-life pattern that is linear is the cost of concert tickets that cost $ each. A real-life pattern that is nonlinear is the area A of a circle with radius r. Copright Big Ideas Learning, LLC

14 Chapter. On Your Own (pp. 7 7) The points do not form a line. So, the function is nonlinear. As increases b 7, decreases b. The rate of change is constant. So, the function is linear.. The points do not form a line. So, the function is nonlinear... The equation = can be rewritten in slope-intercept form =. So, the equation represents a linear function. O The points form a line. So, the function is linear.. The graph is not a line. So, the function is nonlinear. form. So, the equation represents a linear function. As increases b, decreases b. The rate of change is constant. So, the function is linear.. The equation = + is written in slope-intercept 7. The graph is a line. So, the function is linear.. The graph is not a line. So, the function is nonlinear intercept form. So, the equation represents a nonlinear function. nonlinear function does not have a constant rate of change.. The equation = does not belong because it cannot be rewritten in slope-intercept form, whereas the other three equations can be rewritten in slope-intercept form. Practice and Problem Solving. + + As increases b, increases b. The rate of change is constant. So, the function is linear. +. Vocabular and Concept Check. A linear function has a constant rate of change and a +. The equation = cannot be rewritten in slope-. Eercises (pp. 7 7) As increases b, changes b different amounts. The rate of change is not constant. So, the function is nonlinear. The points form a line. So, the function is linear. Copright Big Ideas Learning, LLC

15 Chapter V As increases b, V increases b different amounts. The rate of change is not constant. So, the table represents a nonlinear function r =. Now substitute this value for r in one of the equations for. =. + r =. +. =. So, the missing -value is As decreases b, increases b different amounts. The rate of change is not constant. So, the table represents a nonlinear function.. The equation = r =. The equation can be rewritten in slope-intercept form. So, the equation represents a linear function.. + r =. rise. = =. run the -intercept is. = +. + r =. r 7 So, a linear function is =. +, or =... + = + increase from. to the missing -value must equal the increase from the missing -value to.. Let r be the constant rate. So, =. + r and =. r. Set these to equations equal to each other and solve for r. Because the etended line crosses the -ais at (, ), 7 = +. a. For the table to represent a linear function, the slope = = + 7 cannot be rewritten in slope intercept form. So, the equation represents a nonlinear function. Pounds. + = 7 The equation can be rewritten in slope-intercept form. So, the equation represents a linear function. 7 Cost (dollars) does not change b a constant rate and does not change b a constant rate. So, the table represents a nonlinear function.. Answer should include, but is not limited to: Students will research information about lophones using the Internet or some other reference source. Students will determine the pitches for various lengths of the wooden bars and use this information and the concepts learned in this section to determine whether the pitch of a note is a linear function of the length of the bar.. The formula for the volume of a clinder is V = π r h. The volume of a clinder with a radius of feet is V = π () ( h) = π h. So, the equation is written in slope-intercept form and therefore it represents a linear function. Fair Game Review. The angle measure is greater than and less than. So, the angle is obtuse.. The angle measure is. So, the angle is straight. Copright Big Ideas Learning, LLC

16 Chapter. The angle measure is less than. So, the angle is acute.. The angle measure is. So, the angle is right.. B; + + = Lesson.b + = = Practice (pp. 7A 7B). a. Toenail Growth mm r. mm = r weeks week Toenails grow about. millimeter per week. Fingernail Growth Weeks Fingernail Growth (millimeters) change in growth = change in time.7 mm week Fingernails grow about.7 millimeter per week. So, fingernails grow faster than toenails. Growth (millimeters) Fingernails Toenails Time (weeks).7... The graph that represents fingernails is steeper than the graph that represents toenails. So, fingernails grow faster than toenails.. a. Manager A $ per hour Manager A earns $ per hour. Manager B change in earnings $7 $ = = change in time hours hour Manager B earns $ per hour. So, Manager B has a higher hourl wage. Manager A Hourl Hours Earnings = + Bonus wage worked = + Because the graphs intersect at the point (, ), Manager B will earn more mone than Manager A after hours. Quiz.. (p. 7) rise. slope = = = run... Earnings (dollars) 7 Because the line crosses the -ais at (, ), the -intercept is. So, a linear function is = +. rise slope = = = run Because the line crosses the -ais at (, ), the -intercept is. So, a linear function is =. rise slope = = run Because the line crosses the -ais at (, ), the -intercept is. Manager A Manager B 7 So, a linear function is O Time (hours) (, ) rise slope = = = run = +, or Because the line crosses the -ais at (, ), the -intercept is. So, a linear function is = +. =. Copright Big Ideas Learning, LLC

17 Chapter. rise slope = = run Because the line crosses the -ais at (, ), the -intercept is. So, a linear function is =.. The graph is not a line. So, the function is nonlinear. 7. The graph is a line. So, the function is linear.. The graph is a line. So, the function is linear As increases b, decreases b. The rate of change is constant. So, the function is linear As increases b, increases b different amounts. The rate of change is not constant. So, the function is nonlinear O As increases b, changes b different amounts. The rate of change is not constant. So, the function is nonlinear.. a. rise slope = = = run Because the line crosses the R-ais at (, ), the R-intercept is. So, the linear function is R = A +. R = A + = + = + = ( ) The revenue is $ million when the compan spends $ million on advertising.. The equation = 7. is written in slope-intercept form. So, the equation represents a linear function. Chapter Review (pp. 7 77). Ordered pairs: (,, ) (,, ) (,, ) (, ) The domain is,,, and. The range is,,, and.. Ordered pairs: (,, ) (,, ) (,, ) (,, ) (, ). Revenue (millions of dollars) R The domain is,,,, and. The range is,, and. ( ) = ( ) The domain is,,, and. The range is,,, and.. + = = + = () = ( ) = ( ) + = () + = ( ) 7 A Advertising (millions of dollars) + = () + = The domain is,,, and. The range is,,, and. Copright Big Ideas Learning, LLC

18 Chapter Miles Time can represent an value greater than or equal to. So, the domain is continuous. Cost (, ) (, ) (, ) (, ) (, ) Hours (,.) (,.) Stamps Because ou cannot bu part of a stamp, the graph consists of individual points. So, the domain is discrete. rise slope = = = run Because the line crosses the -ais at (, ), the -intercept is. So, the linear function is =. rise slope = = run Because the line crosses the -ais at (, ), the -intercept is. So, the linear function is (, ) (,.) (,.) O rise slope = = = run = +. Because the line crosses the -ais at (, ), the -intercept is. So, the linear function is = +.. rise slope = = = run Because the line crosses the -ais at (, 7 ), the -intercept is 7. So, the linear function is = 7, or = As increases b, increases b. The rate of change is constant. So, the function is linear As increases b, changes b different amounts. The rate of change is not constant. So, the function is nonlinear.. The graph is not a line. So, the function is nonlinear. Chapter Test (p. 7). Ordered pairs: (, ), (, ), (, ), (, ), (, ). O 7 7 The domain is,,,, and. The range is,, and. 7( ) = ( ) 7 = 7( ) = 7 ( ) = The domain is,,, and. The range is,,, and. Copright Big Ideas Learning, LLC

19 Chapter... Cost (dollars) Because ou cannot have part of a hair clip, the graph consists of individual points. So, the domain is discrete. Gallons Time can represent an value greater than or equal to. So, the domain is continuous. rise slope = = run Because the line crosses the -ais at ( ) -intercept is. So, the linear function is =.,, the As increases b, decreases b. The rate of change is constant. So, the function is linear. 7. a. Words: Amount saved is % of monthl earnings. Variables: Let be the amount saved and let be our monthl earnings. Equation: =. An equation in function form is =... (, ) (,.).. (, ). (,.) Hair clips (, ) (, ) (, ) (, ) Minutes Input,. Output,.( ).7.( )..( )..( ) c. The sum is.. So, the total amount saved is $... Words: Number of cans of food is number of cans per bo times number of boes. Variables: Let be the number of cans of food and let be the number of boes. Function: = A linear function is = S As increases b, S increases b different amounts. The rate of change is not constant. So, the function is nonlinear. Chapter Standardized Test Practice (pp. 7 ). D; Input,. Output,.( ).( ).( ).( ) The range of the function is,,, and.. F; P =. + =. + =. = The batter will be full discharged after = hours of use.. ; Let be the number of hours and be the total cost. (, ) and (, ) rise slope = = = run Total cost (dollars) 7 (, ) (, ) 7 Number of hours The slope is and the -intercept is, so an equation for the total cost is = +. So, the fied cost to rent the limousine is ( ) + = $. Copright Big Ideas Learning, LLC

20 Chapter. B; The graph in part B is not a line, so the function is. Part A: nonlinear. +. H; The value = gives the same -value for both equations. So, the sstem has one solution: (, ).. ; F F F F = = h h h (, ), (, ), (, 7) The domain of the function is,,,,,, and. w. F; w w w = ( w ) = w Perimeter As the side length increases b, the perimeter increases b. The rate of change is constant. So, the function is linear. Part B: Side length Area As the side length increases b, the area increases b different amounts. The rate of change is not constant. So, the function is not linear. = w = + + w =. H; + = w. C; slope = + Side length The temperature fell F each hour. 7. C; Ordered pairs: (, 7), (, ), (, ), (, ), +. B; $. ml $ $. = = L L L ml rise = = run (, ) O 7 slope = rise = run Because the line crosses the -ais at (, ), the -intercept is. So, the linear function is =. = = = Copright Big Ideas Learning, LLC