8 - graphs discrete & continuous domains

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8 - graphs discrete & continuous domains

  1. 1. Discrete & Continuous DomainsHolt Course 3 3.3Glencoe 2-3C
  2. 2. Adults $4.00Children $2.008-2xyor1624 +==+ yxDomain (x-values): 0, 1, 2, 3, 4Range (y-values): 8, 6, 4, 2, 0• The domain is discrete because it hasonly the numbers 0, 1, 2, 3, and 4. Discretegraphs are made up of distinct, orunconnected, points.• Since there is no such thing as half aticket, or one-forth of a ticket the domaindoes not include those points between thepoints graphed.Functions shows a recipes mix of adult & children showtickets.
  3. 3. 8-2xyor1624 +==+ yxDomain (x-values): x ≥ 0 and x ≤ 0(all numbers from 0 to 4)Range (y-values): y ≥ 0 and y ≤ 8(all numbers from 0 to 8)• The domain is continuous because itincludes all numbers from 0 to 4 on thenumber line. Continuous graphs aremade up connected lines or curves.• Cheese can be divided into fractionsor decimals, so it is shown to becontinuous by using a line to include allof those points.Cheddar: $2/lbSwiss: $4/lbFunctions shows a recipes mix of cheddar & Swiss cheese.
  4. 4. •Write a linear function to represent each problem.•Graph the function.•Describe the domain and range of each function. Is thedomain discrete or continuous?You are in charge of reserving hotel rooms for abaseball team. Each room costs $69, plus $6 tax, pernight. You need each room for two night. You need 10to 16 rooms. Write a function for the total hotel costs.yx =150
  5. 5. 1500)10(150 =1650)11(150 =1800)12(150 =1950)13(150 =1050)14(150 =2250)15(150 =2400)16(150 =Discrete
  6. 6. •Write a linear function to representeach problem.•Graph the function.•Describe the domain and range ofeach function. Is the domain discreteor continuous?The airline you are using for thebaseball trip needs an estimateof the total weight of the team’sluggage. You determine thatthere will be 36 pieces ofluggage and each piece willweigh from 25 to 45 pounds.Write a function for the totalweight of the luggage.1620or x4536x900or x2536≤⋅≤≥⋅≥x
  7. 7. 1620x900x≤≥Continuous
  8. 8. Key Idea• A discrete domain is a set of input values that consistsof only certain numbers in an interval. Like integers 1to 4.• A continuous domain is a set of input values thatconsists of all numbers in an interval. Like all numbers1 to 4.BACK-3 -2 -1 0 1 2 3 4 5-3 -2 -1 0 1 2 3 4 5
  9. 9. The graphs show the speeds of two cars over time.Tell which graph corresponds to each situation.Matching Situations to GraphsMr. Lee is traveling on the highway. He pulls over,stops, then accelerates rapidly as he gets back onthe highway. Graph 2
  10. 10. The graphs show the speeds of two cars over time.Tell which graph corresponds to each situation.Matching Situations to GraphsMs. Montoni slows down as she leaves the main road. Shecontinues to slow down as she turns onto other streetsand eventually stops in front of her house. Graph 1
  11. 11. Check It Out: Example 1ATell which graph corresponds to the situation describedbelow.TimeRunner’sSpeedTimeRunner’sSpeedTimeRunner’sSpeedGraph 1 Graph 2 Graph 3Jamie begins the race, and soon feels a pain in amuscle. He is unable to complete the race.Graph 2—Jamie is unable to complete the race, so hisspeed decreases to zero.
  12. 12. Check It Out: Example 1BTell which graph corresponds to the situation describedbelow.TimeRunner’sSpeedTimeRunner’sSpeedTimeRunner’sSpeedGraph 1 Graph 2 Graph 3Melissa builds up her speed during the beginning of therace. She maintains her running speed for theremainder of the race.Graph 1—Melissa’s speed increases at the beginningand then the graph remains constant.
  13. 13. Create a graph for the situation. Tell whether the graph iscontinuous or discrete.The table showsthe temperatureinside a car overtime.Time 8:00 8:30 12:00 12:30Temp.(F) 71 71 82 74Car Temperature64666870727476788082848:00 8:30 12:00 12:30TimeTemp(F)Creating a Graph of a SituationSince every value oftime has acorresponding altitude,connect the points.The graph is continuous.
  14. 14. Create a graph for the situation. Tell whether the graph iscontinuous or discrete.A market sells pumpkinsfor $5 each.Pumpkin Cost05101520253035400 2 4 6 8Pumpkins PurchasedCost($)Creating a Graph of a SituationThe cost (y-axis)increases by $5 for eachpumpkin purchased (x-axis).Because each person canonly buy whole pumpkinsor none at all, the graphis distinct points.The graph is discrete.
  15. 15. Create a graph for the situation. Tell whether the graph iscontinuous or discrete.The table showsthe distance traveledduring a family vacation.Distance TravelledExample 2ASince every value oftime has acorresponding altitude,connect the points.The graph is continuous.Time 8:00 10:00 12:00 2:00Distance (mi) 280 320 500 58001002003004005006007008:00 10:00 12:00 2:00TimeDistance(mi)
  16. 16. Lesson QuizTell which graph corresponds to the situation. Then tellwhether the graph is continuous or discrete.A bus pulls out from the gas station. It drives to its first stop.Then the bus gets on the expressway.Graph B; continuous
  17. 17. 1. Maggi has $25 in her bank account. She gets $5 every dayfrom her father and deposits the money in the account forthe first three days. On the fourth day, she buys a hat forherself with the money. Identify the table thatcorresponds to this situation.A. B.Lesson Quiz for Student Response Systems
  18. 18. Discrete & Continuous DomainsHolt Course 3 3.3Glencoe 2-3C

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