Skills Practice Skills Practice for Lesson 1.1

Transcription

1 Skills Practice Skills Practice for Lesson. Name Date Human Growth Multiple Representations of Relations and Functions Vocabular Discuss the similarities and differences between each set of terms.. relation and function. domain and range Problem Set Create a scatter plot of the relation defined b each table. Then determine if each relation is a function.. Da Inches of Rain O Yes, the relation is a function. Chapter l Skills Practice 6

2 . Da Average Temperature Da Average Humidit 90% 0% 0% 80% 90% 6 80% 7 90% 8 0%. Da Average Pressure Chapter l Skills Practice

3 Name Date Determine the domain and range of each relation. Then use the scatter plot to make the prediction.. The scatter plot shows the relation between the ages of trees in ears and their heights in feet. Predict the average height of a tree that is 6 ears old. The domain is all ages between ear and 0 ears. The range is all heights between feet and 8 feet. The average height of a tree that is 6 ears old is about 7 to 8 feet. Height (feet) Age (ears) The scatter plot shows the relation between the ages of trees in ears and the diameters of their trunks in inches. Predict the average diameter of a tree that is ears old. 9 Diameter (inches) Age (ears) 6 8 Chapter l Skills Practice 67

4 7. The scatter plot shows the weekl accumulated snowfall, in inches, for the 0 weeks of the ski season. Predict the accumulated snowfall after weeks. Weekl accumulated snowfall (inches) Time (weeks) The scatter plot shows the water level in a reservoir given a number of das after the beginning of the ear. Predict the water level at da. 0 Water level (inches) Das of ear Chapter l Skills Practice

5 Name Date 9. The scatter plot shows the relation between the number of people working in a restaurant and the customers average wait time in minutes for a table. Predict the number of people working in the restaurant if a customer s average wait time for a table is 0 minutes. Average wait time (minutes) No. of people working The scatter plot shows the relation between the diameter of a tomato in inches and its weight in pounds. Predict the diameter of a pound tomato...0 Tomato weight (pounds) Tomato diameter (inches). Chapter l Skills Practice 69

6 . The scatter plot shows the cost of heating swimming pools of different sizes in gallons. Predict the size of the pool if it costs $00 to heat it Cost to heat pool (dollars) ,000,000 0,000,000 Pool capacit (gallons). The scatter plot shows the cost of heating a swimming pool for different values of the average air temperature. Predict the average temperature if the pool costs $00 to heat Cost (dollars) Average temperature ( F) Chapter l Skills Practice

7 Name Date Write an algebraic equation to model each situation. Define the variables used in the equation.. Marissa has just been offered a new job. If she accepts the offer, she will receive a $0 signing bonus, plus a salar of $00 per week. 00 0, where represents the amount of mone in dollars that Marissa makes in her new job after weeks. To lease a new car, it will cost an initial pament of $,000 plus $ per month.. Eric has 00 tickets at the beginning of his time at the amusement park. Ever time he rides on one of the attractions, it will cost him tickets. 6. Willa is going to knit a sweater. It cost her $0 for the pattern for the sweater, and it costs $6 for each ball of arn she uses to knit the sweater. Use the given information to complete each table. 7. Prints U is a printing compan that can print a compan s name or logo on various office supplies, such as pens, mugs, and mousepads. Your boss would like to order mugs with the compan s logo. Prints U charges a one-time printing fee of $ plus $.0 per mug ordered. Use this information to complete the table. Number of Mugs Ordered Total Cost (dollars) Chapter l Skills Practice 7

8 8. DVDs R Us charges a $0 membership fee and then sells DVDs for $9 each. Use the information to complete the table. Number of DVDs Ordered 0 00 Total Cost (dollars) 9. After spending hours to set up his lathe and other woodworking equipment, it takes Mario minutes to create a wooden candlestick. Use this information to complete the table. Number of Hours Working 0 0 Number of Candlesticks 0. Darren has a $600 credit at the clothing store. Each shirt costs $. Use this information to complete the table. Number of Shirts Bought 0 0 Remaining Credit (dollars) 7 Chapter l Skills Practice

9 Skills Practice Skills Practice for Lesson. Name Date Down and Up Linear and Absolute Value Functions Vocabular Match each term with its corresponding definition.. linear function a. the unit rate of change of a linear function. slope b. the sort of smmetr that eists when a graph has two parts that are mirror images of each other. etreme points c. an function that contains an absolute value epression, such as. absolute value function d. a function whose graph is a line. line smmetr 6. line of smmetr e. in a graph that has line smmetr, this is the line that divides the graph into two mirror images f. the maimum and minimum points of a function Chapter l Skills Practice 7

10 Problem Set Write a linear function to model each problem situation. Define the variables used in the function.. A swimming pool that can hold 0,000 gallons of water is empt. It will be filled continuousl at a rate of 000 gallons per hour until it is full. Let t represent the time in hours and let w represent the amount of water in the pool in gallons. w 000t. A helium-filled balloon has a volume of 000 cubic inches. It graduall loses its helium at a rate of 0 cubic inches per hour until all of the helium is gone.. An elevator starts at the 0th floor, 00 feet above ground level, and goes down at a rate of 0 feet per second.. The temperature of a room is 0 degrees Fahrenheit when a heater is turned on and heats the room at a rate of degrees per hour. Write an absolute value function to model each problem situation. Define the variables used in the function.. A 0-gallon fish tank is emptied at a rate of 0 gallons per hour and then filled back up at the same rate until it is full. Let t represent the time in hours and let w represent the amount of water in the fish tank in gallons. w 0 0t 7 Chapter l Skills Practice

11 Name Date 6. An elevator starts at the 0th floor, 00 feet above the ground, and it goes down at a rate of 0 feet per second until it reaches the ground, at which point it heads back up at a rate of 0 feet per second. 7. The temperature in a room is 0 degrees Fahrenheit when a heater is turned on that warms the room at a rate of degrees per hour until the room is 7 degrees. At that point the heater is turned off and the temperature drops at degrees per hour. 8. A swimming pool that holds 0,000 gallons of water begins full and loses water at the rate of 000 gallons per hour until it is half full, at which point water is added back into the pool at a rate of 000 gallons per hour. Identif the constants in each function. Then determine what each constant means in terms of the problem situation. 9. A swimming pool is full and is read to be drained. The function 8, represents the amount of water in gallons in the swimming pool after it has been draining for hours. The constants are 8,000 and 000. The constant 8,000 represents the amount of water in the pool at time 0 hours, or when the pool is full. The constant 000 represents the rate at which the pool drains in gallons per hour. The negative sign indicates that the pool is draining. 0. A room is being heated. The function T 0 t represents the temperature of the room in degrees Fahrenheit after it has been heated for t hours. Chapter l Skills Practice 7

12 . A hot-air balloon is being filled. The function V 00t represents the volume in cubic feet of hot air in the balloon after t minutes of being filled.. A plane is descending for a landing. The function A 0, t represents the altitude of the plane in feet after it has been descending for t minutes. Use the given information to complete each table.. A silo holds 0,000 bushels of grain. When the silo is full, a conveer is turned on, and the grain is emptied out of the silo b the conveor at a rate of 70 bushels per hour. Time (hours) Amount of Grain Left in Silo (bushels) 0 0,000 6,0,000 6,000 60, A stadium is at its full capacit of 60,000 people. At the end of the game, the crowd eits the stadium at a rate of 00 people per minute. Time (minutes) 0 8 Number of People 76 Chapter l Skills Practice

13 Name Date. A plane fling at 0,000 feet begins to ascend at a rate of 00 feet per minute until it reaches 0,000 feet. Time (minutes) Altitude (feet) 6. James has $00 in his savings account, and he decides to deposit $ each week into the account. Time (weeks) Balance (dollars) Graph each function. Determine the domain, range, and etrema of each function. 7. Domain: all real numbers Range: all real numbers Etrema: none O Chapter l Skills Practice 77

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17 Skills Practice Skills Practice for Lesson. Name Date Let s Take a Little Trip with Me! Ever Graph Tells a Stor Vocabular Define each term in our own words.. interval of increase. interval of decrease. vertical motion. quadratic function Chapter l Skills Practice 8

18 Problem Set Each graph represents the distance in miles a person is from home versus the amount of time in hours the have traveled. Describe the function in words, being sure to include the domain and range and how the distance changed from hour to hour.. John sets out for a walk along the beach earl in the morning and returns seven hours later. The domain is (0, 7), which means that the trip lasted for 7 hours. The range is (0, 7), which means that John traveled 7 miles down the beach. John traveled miles in his first hour and more miles in his second hour, then rested for an hour, and traveled miles during the net hour. Then he turned back, traveling miles in the first hour, miles in the net, and miles in the net, which brought him back to his starting point. Distance (miles) Time (hours). Peton takes her dog for a long walk on Saturda, stopping at different places along the wa. Distance (miles) Time (hours) 8 Chapter l Skills Practice

19 Name Date. Tona decides to walk to her friend Aleandra s house, which is 9 miles awa, sta awhile, and come back home. 0 9 Distance (miles) Time (hours). Tim decides to walk to his friend Ran s house, which is 0 miles awa, spend some time there, and come back home Distance (miles) Time (hours) Chapter l Skills Practice 8

20 Sketch the graph of each function O Chapter l Skills Practice

21 Name Date Determine the intervals of decrease and increase for each function Interval of decrease: (, ) Intervals of increase: (0, ), (, 8) O O 6 Chapter l Skills Practice 8

22 Determine the domain and range of each function shown in the graph O O 6 Domain: all real numbers Range: all real numbers greater than or equal to O O Chapter l Skills Practice

23 Name Date Determine the etreme point and the line of smmetr of each function shown in the graph = O 6 7 O (, ) Minimum at (, ) Line of smmetr: O 6 6 O Chapter l Skills Practice 87

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25 Skills Practice Skills Practice for Lesson. Name Date Building a Better Bo Cubic and Indirect Variation Functions Vocabular Provide two eamples of each term.. cubic function. indirect variation function Problem Set Use the given information to complete each table with the appropriate measurements.. You are building a rectangular wading pool in our ard. You have enough materials so that the length and width of the pool, when added together, will total 0 feet. You want the depth of the pool to be half of the width of the pool. Complete the table for possible widths, lengths, depths, and volumes for the wading pool. Width (feet) Length (feet) Depth (feet) Volume (cubic feet) Chapter l Skills Practice 89

26 . You are building a rectangular tool shed. You have decided that the perimeter of the tool shed will be feet and that the tool shed will be twice as tall as it is wide. Complete the table for possible widths, lengths, depths, and volumes for the tool shed. Width (feet) Length (feet) Height (feet) Volume (cubic feet) You are designing a shipping crate. The perimeter must be 6 feet, and the crate must be one and a half times as tall as it is wide. Complete the table for possible widths, lengths, depths, and volumes for the shipping crate. Width (feet) Length (feet) Height (feet) Volume (cubic feet) You are building a warehouse. The length and width should add up to 00 feet, and the height should be equal to half the width. Complete the table for possible widths, lengths, depths, and volumes for the warehouse. Width (feet) Length (feet) Height (feet) Volume (cubic feet) Chapter l Skills Practice

27 Name Date Use the given table to create a scatter plot for the relation between the width and volume.. You are building a small bo in the shape of a rectangular prism to hold our jewelr. You have decided that the perimeter of the base of the bo will be 8 inches and that the bo will be half as tall as it is wide. The table below includes some possible dimensions for the bo. Width (inches) Length (inches) Height (inches) Volume (cubic inches) Volume (cubic inches) Width (inches) 6. You are designing a large chest in the shape of a rectangular prism to store our tools. The perimeter of the base must be 0 feet, and the chest must be as tall as it is wide. The table below includes some possible dimensions for the chest. 8 9 Width (feet) Length (feet) Height (feet) Volume (cubic feet) Chapter l Skills Practice 9

28 7. You are constructing a small building in the shape of a rectangular prism to house a manufacturing assembl line. The sum of the length and width should be 0 feet, and the height should be. times the width. The table below includes some possible dimensions for the building. Width (feet) Length (feet) Height (feet) Volume (cubic feet) ,000 8, , , , You are building a holding pond in the shape of a rectangular prism to hold runoff water after a storm. You have enough materials so that the length and width of the pond, when added together, will total 60 feet. You want the depth of the pond to be two-thirds the width of the pond. The table below includes some possible dimensions for the holding pond. Width (feet) Length (feet) Depth (feet) Volume (cubic feet) , ,8, ,0, ,608, ,600, Chapter l Skills Practice

29 Name Date Use the given information to complete each table with the appropriate measurements. 9. A floor installer has 00 square feet of hardwood flooring. Complete the table with the possible lengths of a rectangular room that can be completel filled with 00 square feet of hardwood flooring. Width (feet) Length (feet) Width (feet) Length (feet) A wallpaper installer has 80 square feet of wallpaper to put on one rectangular wall. Complete the table with the possible widths of a rectangular wall that can be completel filled with 80 square feet of wallpaper. Height (feet) Width (feet) Height (feet) Width (feet) A rancher needs 80 square feet of grass to graze a single sheep. Complete the table with the possible lengths of a rectangular field that is 80 square feet. Width (feet) Length (feet) Width (feet) Length (feet) Chapter l Skills Practice 9

30 . A gallon of paint will cover 60 square feet. Complete the table with the possible lengths of a rectangular wall that can be completel covered with a gallon of paint, assuming one coat of paint is used. Height (feet) Length (feet) Height (feet) Length (feet) Use the given information to write an equation that models the situation.. A bo s height is two inches more than its width, and its length is two inches more than its height. Write an equation describing the bo s volume in terms of its width. V w(w )(w ) w 6w 8w. A swimming pool s width is two feet more than half its length, and its depth is half its width. Write an equation describing the pool s volume in terms of its length.. A gardener has 00 square feet of sod that he wishes to set out in a rectangular area. Write an equation to represent the width of the rectangle that can be covered b 00 square feet of sod. 9 Chapter l Skills Practice

31 Name Date 6. A gallon of stain covers 00 square feet of a rectangular wooden fence. What is the length of fence that can be painted with a gallon of stain in terms of its height? 7. The perimeter of a rectangular swimming pool is 80 feet, and its depth is one-half its width. What is an equation that describes the swimming pool s volume in terms of its width? 8. A cardboard bo has a width and a length that add up to 6 inches, and its height is twice its width. What is an equation that describes the bo s volume in terms of its width? 9. Charlie likes to pace in a rectangular pattern. If each of his paces is two feet long, and he takes 00 steps to pace out an entire rectangle, write an equation for the area of the rectangle that he paces in terms of the length of one of the sides. Chapter l Skills Practice 9

32 0. Marcia is fencing off her rectangular garden. She has 80 feet of fencing. What is an equation for the area of the garden in terms of the length of one of the sides? Use the given information and the graph to answer the question.. A rectangular water trough for horses is to be built such that the width and length add up to 6 feet and the depth is to be foot more than the width. The volume of the trough is given b the formula V w w 6w, where w represents the width of the trough, and the graph of the function is given below. What is the largest approimate volume of the horse trough? Because onl positive numbers make sense for the length, we consider onl the numbers between 0 and 6, and it looks as though the function has a maimum of about 0, somewhere around w. So the maimum volume is around 0 cubic feet. v w 96 Chapter l Skills Practice

33 Name Date. Jack is building a wooden chest to store his clothes. The sum of the width and length of the chest total 8 feet, while its height is the same as its width. The volume of the chest is given b the formula V w 8w, where w represents the width of the chest, and the graph of the function is given below. What is the largest approimate volume of the chest? v w 0. Suzanne has 6 square feet of flooring that she will put down in a rectangular pattern with a width w. The length of the room that can be covered with that much flooring is given b l 6 w, and the graph of the function is given below. Looking at the graph, what can ou sa about the maimum length of the room covered with the flooring? l w Chapter l Skills Practice 97

34 . Federico is mapping out a garden area. It will have 00 square feet with a width of w and a length given b the formula l 00 w. The graph of the function is given below. Looking at the graph, what can ou sa about what happens to the length of the garden as the width gets larger? l w 0 98 Chapter l Skills Practice