Discrete and Continuous Domains

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. Discrete and Continuous Domains How can ou decide whether the domain of a function is discrete or continuous? EXAMPLE: Discrete and Continuous Domains In Activities and in Section., ou studied two real-life problems represented b the same equation. + = a. or = + 9 = + onl points on the graph 9 Domain (-values):,,,, Range ( -values):,,,, The domain is discrete because it consists of onl the numbers,,,, and. b. 9 = + all points on line segment COMMON CORE Functions In this lesson, ou will graph discrete and continuous data. determine whether functions have a discrete or continuous domain. Learning Standards.F. F.IF. F.IF. Chapter Domain (-values): 9 Range ( -values): The domain is continuous because it consists of all numbers from to on the number line. Linear Functions

Math Practice Appl Mathematics How can ou use mathematics to represent and solve each problem? ACTIVITY: Discrete and Continuous Domains Work with a partner. Write a function to represent each problem. Graph each function. Describe the domain and range of each function. Is the domain discrete or continuous? a. You are in charge of reserving er b. The airline ou are using for the hotel rooms for a outh soccer soccer trip needs an estimate of team. Each room costs $9, plus the total weight of the team s $ ta, per night. You need each luggage. You determine that there room for two nights. You need will be pieces of luggage and to rooms. Write a function each piece will weigh from to for the total hotel cost. pounds. Write a function for the total weight of the luggage. Total hotel cost Hotel Reservations 9 Number of rooms Total weight of luggage Luggage Weight Pounds per piece. IN YOUR OWN WORDS How can ou decide whether the domain of a function is discrete or continuous? Describe two real-life eamples of functions: one with a discrete domain and one with a continuous domain. Use what ou learned about discrete and continuous domains to complete Eercises and on page. Section. Discrete and Continuous Domains

. Lesson Lesson Tutorials Ke Vocabular discrete domain, p. continuous domain, p. Discrete and Continuous Domains A discrete domain is a set of input values that consists of onl certain numbers in an interval. Eample: Integers from to A continuous domain is a set of input values that consists of all numbers in an interval. Eample: All numbers from to Total cost (dollars) EXAMPLE Museum Tickets (,.) (,.) (,.9) (,.9) (, ) Number of tickets Graphing Discrete Data The function =.9 represents the cost (in dollars) of tickets for a museum. Graph the function using a domain of,,,, and. Is the domain discrete or continuous? Eplain. Make an input-output table. Input,.9, Ordered Pair, (, ).9() (, ).9().9 (,.9).9().9 (,.9).9(). (,.).9(). (,.) Plot the ordered pairs. Because ou cannot bu part of a ticket, the graph consists of individual points. So, the domain is discrete.. The function m = 9d represents the amount of mone m (in dollars) ou have after buing d DVDs. Graph the function. Is the domain discrete or continuous? Eplain. Chapter Linear Functions

Calories consumed EXAMPLE Cereal Bar Calories c (, ) (, 9) (, ) (, ) (, ) Number of bars eaten b Graphing Continuous Data A cereal bar contains calories. The number c of calories consumed is a function of the number b of bars eaten. Graph the function. Is the domain discrete or continuous? Make an input-output table. Input, b, c Ordered Pair, ( b, c ) (, ) (, ) (, ) 9 (, 9) (, ) Plot the ordered pairs. Because ou can eat part of a cereal bar, b can be an value greater than or equal to. Draw a line through the points. So, the domain is continuous. EXAMPLE Real-Life Application Input Time, t (seconds) Distance, d (miles)..... You conduct an eperiment on the speed of sound waves in dr air at F. You record our data in a table. Which of the following is true? A The domain is t and it is discrete. C The domain is. d. and it is discrete. B The domain is t and it is continuous. D The domain is. d. and it is continuous. The domain is the set of possible input values, or the time t. The time t can be an value from to. So, the domain is continuous. The correct answer is B. Eercises. A -gallon bathtub is draining at a rate of. gallons per minute. The number g of gallons remaining is a function of the number m of minutes. Graph the function. Is the domain discrete or continuous?. Is the domain discrete or continuous? Eplain. Input Number of Stories Height of Building (feet) Section. Discrete and Continuous Domains

. Eercises Help with Homework. VOCABULARY Eplain how continuous domains and discrete domains are different.. WRITING Describe how ou can use a graph to determine whether a domain is discrete or continuous. 9+(-)= +(-)= +(-9)= 9+(-)= Describe the domain and range of the function. Is the domain discrete or continuous?.. Graph the function. Is the domain discrete or continuous?. Input Bags, Marbles,. Input Years, Height of a Tree, (feet) 9. Input Width, (inches) Volume, (cubic inches). Input Hats, Cost, (dollars)..9 9. ERROR ANALYSIS Describe and correct the error made in the statement about the domain.. YARN The function m =.b represents the amount m of mone (in dollars) that ou have after buing b balls of arn. Graph the function using a domain of,,, and. Is the domain discrete or continuous?. is in the domain. Chapter Linear Functions

. TICKETS The number t of tickets sold at a concert is a function of the ticket cost c. a. Which variable is independent? dependent? b. Is the domain discrete or continuous?. DISTANCE The function =. converts length from meters to feet. a. Graph the function. Which variable is independent? dependent? b. Is the domain discrete or continuous?. LOGIC The area A of the triangle is a function of the height h. Your friend sas the domain is discrete. Is he correct? Eplain. h in.. PACKING You are packing books into a bo. The bo can hold at most books. The function =. represents the weight (in pounds) of books. a. Is in the range? Eplain. b. Is in the domain? Eplain. c. Graph the function. Is the domain discrete or continuous?. Describe a real-world situation for the given constraints. a. A negative number in the domain and the domain is continuous b. A negative number in the range and the domain is discrete Find the slope of the line. (Section.)... 9. MULTIPLE CHOICE What is the -intercept of the graph of the linear equation? (Section.) A B C D Section. Discrete and Continuous Domains

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