THE NEWARK PUBLIC SCHOOLS THE OFFICE OF MATHEMATICS Grade 8 Functions 8.F.1-3 Student Pages 2012 2012 COMMON CORE CORE STATE STATE STANDARDS ALIGNED ALIGNED MODULES
Grade 8 - Lesson 1 Introductory Task CONCERT TICKETS. You are buying concert tickets that cost $15 each. You can buy up to 6 tickets. 1. Write an equation that will give the relationship (function rule) between the amount (in dollars) you spend and the number of tickets you buy. Let Let y the amount you spend x the number of tickets you buy 2. Complete the table below: Number of tickets x 0 1 2 3 4 5 6 Amount in (dollars) y 3. Identify the dependent and independent variables. 4. Then identify the domain and range of the function. 5. What is a function rule? 6. How does the number of tickets affect the total amount spent? Page 2 of 34
Grade 8 - Lesson 1 Guided Practice 1. The input-output table shows the cost of various amount of regular unleaded gas from the same pump. Identify the domain and range of the function. Input (gallons) Output (dollars) 10 12 13 17 19.99 23.99 25.99 33.98 Domain: Range: 2. Identify the domain and range. Input (x) 0 1 2 4 Output (y) 5 2 2 1 Domain: Range: 3. Tell whether the pairing is a function. 4. Tell whether the pairing is a function. (a) (b) Page 3 of 34
5. The domain of the function y 3x is 0, 2, 5, 7, and 8. Make a table for the function. Identify the range of the function. 6. Write a rule for the function. Input (x) 0 1 4 6 10 Output (y) 2 3 6 8 12 Rule: 7. Write a rule for the function. Then identify the domain and range. Time (hours) 1 2 3 4 Pay (dollars) 8 16 24 32 Rule: Domain: Range: 8. MULTIPLE REPRESENTATION You have 10 quarters that you can use for a parking meter. Describing in Words Copy and complete. Each time you put 1 quarter in the meter, you have 1 less quarter, so? is a function of?. Writing a Rule Write a rule for the number of y quarters that you have left as a function of the number of x quarters you have used so far. Identify the domain of the function. Making a Table Make a table and identify the range of the function. Page 4 of 34
In problems 9 and 10, describe and correct the error related to the function represented by the table. Input (x) 1 2 3 4 5 Output (y) 6 7 8 6 9 9. The pairing is not a function. One output is paired with two inputs. 10. The pairing is a function. The range is 1, 2, 3, 4, and 5. Page 5 of 34
Grade 8 - Lesson 1 Collaborative Work 1. MULTIPLE REPRESENTATIONS At a yard sale, you find 5 paperback books by your favorite author. Each book is priced at $.75. a. Describing in Words. Copy and complete: For each book you buy, you spend $.75, so? is a function of?. b. Writing a Rule. Write a rule for the amount (in dollars) you spend as a function of the number of books you buy. Identify the domain of the function. c. Making a Table. Make a table and identify the range of the function. 2. Make a table for the function y x 5 with domain 10, 12, 15, 18, and 29. Then identify the range of the function. Page 6 of 34
3. Identify the domain and range of the function. (a) (b) (c) 4. Tell whether the pairing is a function. (a) (b) (c) Journal Question(s) SAVINGS You have $100 saved and plan to save $20 each month. Write a rule for the amount saved (in dollars) as a function of the number of months from now. Identify the independent and dependent variables, the domain, and the range. How much will you have saved altogether 12 months from now? Page 7 of 34
Grade 8 - Lesson 1 Homework Name: Date: 1. What are the variables in the graph shown? 2. Describe the relationship between time and temperature in the table below. 3. Match one of the labeled segments in the graph below with each of the following verbal descriptions: a. rising slowly b. constant c. falling quickly 4. Do the values in each table represent a linear function? If so, write a function rule. x 2 1 0 1 y 8 5 2 1 (a) x 0 1 2 3 y 8 6 4 2 (b) Page 8 of 34
5. Suppose the rate for a toll-free telephone number is $2.95 per month plus $0.10 per minute of use. Write a function rule that correctly represents the monthly cost. 6. Graph the equation for input values and. 7. Graph the equation for input values and. Page 9 of 34
Grade 8 - Lesson 2 Introductory Task Examine the scatter plot shown. 1. Identify the domain and range of the function. 2. Make a table for the graph. x y 3. Find a relationship between the inputs and the outputs. 4. Write a function rule that describes the relationship. Page 10 of 34
Grade 8 - Lesson 2 Guided Practice 1. Consider the function. a. Make an input-output table with domain 0, 2, 4, 6, and 8. x y b. Plot a point for each ordered pair 2. Write a rule for the function represented by the graph. Identify the domain and the range of the function. (a) (b) 3. CHALLENGE. The graph represents a function. a. Write a rule for the function. b. Find the value of y so that (1.5, y) is on the graph of the function. Page 11 of 34
4. Student council members are raising funds by selling hats. They take a survey to see how many students will buy the hats at different prices. The results are below. Price (dollars) 2 4 6 8 10 12 Number of Buyers 400 325 250 175 100 25 a. Graph the data. (Use the graph paper provided.) b. Use the graph to estimate the number of hats that will be sold at $5. c. How is the number of buyers related to the price of the hats? 5. The table below shows how the value of a car depends upon its age. Age of car new 1 year 2 year 3 year 4 year Value of car $16000 $14800 $13600 $12700 $12025 a. Graph the data. (Use the graph paper provided.) b. Use the graph to estimate the value of the car when the car is 5 years old. c. How is the value of the car related to its age? Page 12 of 34
Grade 8 - Lesson 2 Collaborative Work 1. Consider the function. a. Make an input-output table with domain 1, 2, 3, 4, and 5. x y b. Plot a point for each ordered pair 2. Graph each linear equation. a. b. c. Page 13 of 34
3. Alicia makes necklaces and sells them at jewelry show. She pays $10 to have a table at the show and makes $20 for each necklace she sells. a. Write a function for the money she earns. b. What is the input variable? What is the output variable? c. Graph the function with domain 0, 1, 2, 3, 4, and 5. d. At what point does the graph cross the y-axis? e. How much money would Alicia make if she sold 7 necklaces? 4. Do the values in the table below represent a linear function? If so, write a function rule. x 2 1 0 1 y 8 5 2 1 (a) x 0 2 5 7 y 1 6 12 5 (b) 5. Mrs. Russell receives a weekly base salary of $500, plus a commission of $1,200 on each car that she sells. Write a function rule relating her total weekly pay p to cars she sells c. Page 14 of 34
Journal Question(s) SAT SCORES The table shows the average score s on the mathematics section of the Scholastic Aptitude Test (SAT) in the United States from 1997 to 2003 as a function of the time t in years since 1997. In the table, 0 corresponds to the year 1997, 1 corresponds to 1998, and so on. Years since 1997, t 0 1 2 3 4 5 6 Average score, s 511 512 511 514 514 516 519 1. Graph the function. (Choose a scale that allows you to plot the points on a graph that is a reasonable size.) 2. Suppose you use a scale on the s-axis from 0 to 520 in increment of 1 unit, describe the appearance of the graph Page 15 of 34
Grade 8 - Lesson 2 Homework Name: Date: 1. The cost of several oranges at $0.10 each is a function of the number of oranges you buy. a. Complete the table. number you buy 1 2 6 12 cost.10 b. Graph the function using the table. c. Write a function rule relating C to n. d. How much would 25 oranges cost? e. How many oranges could $6.40 buy? 2. Complete the statement(s): a. If, then is a function of?. b. If, then is a function of?. Page 16 of 34
3. a. Complete the table. Rate (km/h) 10 20 30 40 Distance (km) 40 b. Write a function rule relating distance to rate. c. Determine the distance covered if the rate is 60 km/h. d. Determine the rate if the distance covered is 180 km. Page 17 of 34
Grade 8 - Lesson 3 Introductory Task The functions below represent pricing plans for car rentals, where d is number of days and C is cost. Which plan is best? Explain your reasoning. Subcompact: Total cost is $30 plus $25 per day. Compact: 7d 0.25C 10 Luxury: Page 18 of 34
Grade 8 - Lesson 3 Guided Practice 1. Which function has a greater rate of change? 3y 6 12 x 1 2 3 4 y 5 8 11 14 2. Determine which function has a greater rate of change. y 3x 4 x 1 2 3 4 y 8 10 12 14 3. Which function has a greater rate of change? 1 8 1 y x 2 3 4 x 0 2 4 6 y -4 6 16 26 4. Order functions A, B, C, and D from least to greatest rate of change. HINT: Find the slope for each function. a. b. x 2 0 2 4 y 7 9 11 13 Page 19 of 34
c. d. As x increases by 3 units, y increases by 2 units. 5. John and Paul each have a savings account. John deposited $500 and withdrew $25 each week for 8 weeks. Paul opened his account with $150 and deposits $150 each week for the next 6 weeks. a. Compare John s account to Paul s account. b. Complete a table showing John s savings for the 8 weeks. c. Complete a table showing Paul s savings for the 8 weeks d. Plot the data you obtained on the same x-y coordinate plane. (Use the graph paper provided.) e. What is the point of intersection? What is the significance of this point? Page 20 of 34
Grade 8 - Lesson 3 Collaborative Work 1. Order functions A, B, and C from least to greatest rate of change. HINT: Find the slope for each function. a. b. x 4 0 4 8 y 2 3 4 5 c. As x increases by 3 units, y increases by 1 unit. 2. In the diagram below, what is the relationship between the number of rectangles and the perimeter of the figure they form? Represent this relationship using a table words a function rule and a graph. Page 21 of 34
3. Luigi s Pizza charges $8 for a large pizza and $0.75 for each topping. a. Luigi s Pizza offers 10 toppings. Create an input-output table for the total cost C (in dollars) of a pizza as a function of the number n toppings. Explain why the table represents a function. b. Describe the domain and range of the function. c. Write an equation or function rule for the total cost C (in dollars) with n toppings. d. You have $11 to spend on a large pizza. What is the greatest number of toppings you can afford? Page 22 of 34
(23 and 17). (14 and 2 Journal Question(s) $6 per car The Math Club is planning a car wash. They need $70 worth of materials. a. Use a verbal model to write an equation that relates their profit to the numbers of cars the Math Club washes.. b. Find their profit if the Math Club washes 120 cars. c. Does doubling the number of cars they wash double their profit? Explain Page 23 of 34
. Grade 8 - Lesson 3 Homework Name: Date: 1. Order stocks from greatest to least according to the rate of price increase. HINT: Find the slope for each function. a. Beta Co. A starting price of $54, decreases weekly by $2.50. b. Alpha, Inc. Week 0 1 2 3 4 Prices($) 16 19 22 25 28 c. Delta Corp. Week 0 1 2 3 4 Prices($) 21 16.5 12 7.5 3 d. Gamma Inc. (w is weeks, d is dollars) 2. In the diagram below, what is the relationship between the number of triangles and the perimeter of the figure they form? Represent this relationship using a table words a function rule and a graph. Page 24 of 34
3. Tell whether the pairing of x and y values is necessarily a function. Explain your reasoning. a. Your doctor records your height in x ( in inches) and your weight y (in pounds) each time you have a medical exam. b. Mrs. Eatman, the algebra 1 teacher, makes a table that lists the number of letters in the first name (x) and the number of letters (y) in the last name of each student in her class. Page 25 of 34
Grade 8 - Lesson 4 Introductory Task Tell whether each relationship is linear or nonlinear. a. The relationship between the perimeter P of a square and the length s of one side. b. The relationship between the perimeter A of a square and the length s of one side c. Write and graph an equation for P as a function of s. d. Write and graph an equation for A as a function of s. Page 26 of 34
Grade 8 - Lesson 4 Guided Practice 1. GEOMETRY. An equation for the volume V of a cube with edge length s is. A graph of the equation is also shown. a. What is the reasonable domain for this function? b. Is the relationship between volume and edge length linear or nonlinear? Explain. 2. Tell whether each is a linear or nonlinear relationship. (a) (b) (c) Page 27 of 34
3. Tell whether the relationship between the radius r and each given variable is linear or nonlinear. a. Circumference C b. Area A c. Volume V 4. Graph each of the tables below. Then determine whether the function is linear. If so, write a rule for the function. x 3 4 5 6 7 y 19 25 31 37 43 x 0 1 2 3 y 2 6 18 54 162 (a) (b) 5. Sketch a graph to represent each situation. Label each section. a. hours of daylight each day over the course of the year b. your distance from the ground as you ride a ferris wheel c. your pulse rate as you watch a scary movie Page 28 of 34
Grade 8 - Lesson 4 Collaborative Work Solve the problems given below. 1. Graph each of the tables below. Then determine whether the function is linear. If so, write a rule for the function. x 4 2 0 2 4 y 1 0 1 2 3 (a) x 1 2 3 4 y 10 7 4 1 2 (b) 2. Determine whether the function is linear or non-linear. Explain your answer. a. b. c. 3. Select the non-linear function. Explain your choice(s). a. b. c. d Page 29 of 34
4. Use the diagram below to find the relationship between the number of shapes and the perimeter in each stage Stage 1 Stage 2 Stage 3 a. Represent the relationship using a table words an equation, and a graph. b. Is the relationship linear or non-linear? Explain. 5. How can you tell from a table, graph, or an equation if a functional relationship is linear or non-linear? Page 30 of 34
Journal Question(s) Find two examples of real world relationships that can be modeled with graph, one linear and one nonlinear. Model each relationship with a graph
Grade 8 - Lesson 4 Homework Name: Date: Solve each of the problems. Show your steps. 1. Use a table, an equation, and a graph to represent each relationship. a. Antonio is two years older than Bruce. b. Gina makes 3 bracelets per hour. 2. Use the diagram below to find the relationship between the number of hexagons and the perimeter in each stage. Stage 1 Stage 2 Stage 3 a. Represent the relationship using a table words an equation, and a graph. Page 32 of 34
b. Is the relationship linear or non-linear? Explain. 3. For each table, determine whether the relationship is linear function. Then represent the relationship using words, an equation, and a graph. x y 0 5 1 8 2 11 3 14 x y 0 43 1 32 2 21 3 10 (a) (b) Page 33 of 34
Grade 8 - Lesson 5 Golden Problem The Athletics Department needs to decide on the ticket for a basketball game. They estimate that about 500 people will buy ticket if the ticket price is $3. Based on previous games, they estimate that for every $0.50 increase in the ticket, they will sell 50 fewer tickets. a. Copy and complete the table. EXPECTED INCOME from TICKET SALES Ticket Price (dollars) Number of tickets sold Income (dollars) 3.00 500 1500 3.50 450 1575 4.00 4.50 5.00 b. Graph the relationship between the ticket price and the number of tickets sold. Label and scale the axes appropriately. Let x = ticket price and let y = number of tickets sold. Use the grid paper provided. c. Do you think the relationship between ticket price and the number of tickets sold is linear? Explain your reasoning. d. On a separate grid paper, graph the relationship between the ticket price and the income. Label and scale the axes appropriately. Let x = ticket price and let y = income earned in dollars. e. Do you think the relationship between ticket price and income is linear? Explain your reasoning. f. Assume that the estimates are accurate. What price would you charge for a ticket? Give a reason for your answer. Page 34 of 34