0.3 Domain and Range: Relations vs Functions, Domain, Range, and Vertical Line Test Worksheet 3 #1-7

Transcription

1 Unit 0 Check Sheet Function Families Check sheet must be turned in to receive Homework & Quiz points. All quiz corrections must be done for test score to replace quiz scores. No check sheet = No Points. Write quiz scores as fractions Lost Quizzes count as a 0. Section Name Per (Print) Quiz ratio is total points scored on quizzes and pre-test out of total possible Order (from top to bottom) o Check sheet, o Quiz 1, 2, Pre-Test o Quiz corrections 0.1 Graph Activity: Sort group graphs into a minimum of five groups. Explain why you grouped them that way. Discuss left-to-right behavior using increasing, decreasing, constant, and the names of the function families 0.2 Equations of Function Families: Use Desmos to graph functions Worksheet 2 # Domain and Range: Relations vs Functions, Domain, Range, and Vertical Line Test Worksheet 3 # Review Graphs and Equations Flash Cards: Use: linear, discrete, v-shaped, u-shaped, continuous, absolute maximum, absolute minimum, constant, smooth curve, piecewise, increasing, decreasing, symmetry Worksheet 4 #1-22 Quiz Determining the Independent and Dependent quantities Worksheet 5 # Matching word problems to a set of graphed functions Worksheet 6 #1-12 Quiz 2 Pre-Test 0.7 Review Worksheet Review #1-12 Test HMK Quiz 1: Score/Possible Quiz 2: Score/Possible Pre-Test: Score/Possible Total Quiz Ratio: Total Score/Total Possible

2 Name: Date: Period: Worksheet 2 Use to explore the equation cards with the graph cards. Sketch the graph of each function. For each sketch, choose which function family it belongs in from these choices: Piecewise, Exponential, Linear, Quadratic, or Absolute Value Also, decide which characteristics describe the function family (select all that apply): Increasing, Decreasing, Constant, Discrete, Continuous, U-Shaped, V-Shaped, Maximum, Minimum, or Smooth Curve Equation Function Family & Characteristics Sketch 1. yy = 3 2. xx = 2 3. yy = xx ff(xx) = 1 2 xx 4 5. ff(xx) = 0

3 6. ff(xx) = 3 xx yy = xx ff(xx) = (xx 5) 2 9. ff(xx) = xx 2 + 3xx yy = xx 11. ff(xx) = 3xx yy = 1 xx + 1 3

4 13. ff(xx) = 2 xx 14. ff(xx) = 1 4 xx 15. ff(xx) = 5 xx 16. yy = 0.5 xx 3 3xx 1, xx > ff(xx) = xx 9, xx Optional BONUS! ff(xx) = 2 xx x = { -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6 }

5 Name: Date: Period: Vocabulary Relation: Worksheet 3 Domain: Range: Examples Use the points on each graph to complete the corresponding table of values. Graph A x Y Graph B x Y 1. Which graph has a different x-value for each y-value? 2. Which graph has the same x-values for different y-values? 3. If the equation x = 2 were drawn on both graphs, how many points on each graph would intersect this line? Vocabulary Function: Vertical Line Test:

6 Directions: Use the graphs to answer the questions. 4. a. Identify the domain b. Identify the range c. Is the relation a function? 5. a. Identify the domain b. Identify the range c. Is the relation a function? 6. a. Identify the domain b. Identify the range c. Is the relation a function? 7. a. Identify the domain b. Identify the range c. Is the relation a function?

7 Name: Date: Period: Worksheet 4 Directions: Choose the appropriate function family or families to complete each sentence based on the given characteristic(s). Linear Functions Linear Absolute Value Functions Quadratic Functions Exponential Functions 1. The graph of this function family is a straight line. The function family is. 2. The graph of this function family has an increasing interval and a decreasing interval. The function family is. 3. The graph of this function family has an absolute minimum. The function family is. 4. The graph of this function family is decreasing over the entire domain. The function family is. 5. The graph of this function family forms a V shape. The function family is. 6. The graph of this function family has an increasing interval and a decreasing interval and forms a U shape. The function family is. 7. The graph of this function family does not have an absolute maximum or absolute minimum and is a smooth curve. The function family is. 8. The graph of this function family has an absolute maximum or absolute minimum and is made up straight lines. The function family is. 9. The graph of this function family is made up straight lines and does not have an absolute maximum or absolute minimum. The function family is. 10. The graph of this function family decreases over the entire domain and is a smooth curve. The function family is.

8 Directions: Create an equation and sketch a graph for a function with each set of given characteristics. Use values that are any real numbers between -10 and Create an equation and sketch a graph that: 12. Create an equation and sketch a graph that: is a smooth curve, is linear, is continuous, has a minimum, and is discrete, and is decreasing across the entire domain. is quadratic. Equation: Equation: 13. Create an equation and sketch a graph that: 14. Create an equation and sketch a graph that: is a smooth curve, has a maximum, is increasing across the entire domain, is continuous, and is continuous, and is a linear absolute value function. is exponential. Equation: Equation:

9 15. Create an equation and sketch a graph that: 16. Create an equation and sketch a graph that: is linear, is discrete, is continuous, is neither increasing nor decreasing across the entire domain, and does not pass through the origin. has a maximum, does not pass through the origin, and is quadratic. Equation: Equation: Directions: Choose the graph that represents each function. 17. ( ) 18. ( )

10 19. ( ) 20. ( ) 21. ( ), x={...,-1.5, -1, -0.5, 0, 0.5, 1, 1.5,...} 22. ( )

11 Name: Date: Period: Vocabulary Independent Quantity: Dependent Quantity: Worksheet 5 Example The number of hours worked and the amount of money earned. independent quantity dependent quantity Quantities vs. Units The QUANTITY is what is being measured (ex: time, weight, distance, etc.) The UNITS are how the quantities are being measured (ex: seconds, gallons, miles, etc.) Discrete vs. Continuous Data DISCRETE DATA are quantities that can only be represented at isolated values (ex: people, number of t-shirts, number of cars washed). They are graphed as Dotted data. CONTINUOUS DATA are quantities that can be represented over an interval of values (ex: rate of change, amount of money being earned, time). They are graphed as Solid data. Determine the independent and dependent quantities. 1. The domain is made up of x-values and the range is made up of y-values Independent quantity: Dependent quantity: 2. Your grade on a test and the number of hours you studied. Independent quantity: Dependent quantity: 3. Selena is driving to visit her grandmother who lives 325 miles away from Selena s home. She travels an average of 60 miles per hour. If the dependent quantity is the distance traveled, what is the independent quantity? Independent quantity: 4. Benjamin works at a printing company. He is making T-shirts for a high school volleyball team. The press he runs can imprint 3 T-shirts per minute with the school s mascot. If the independent quantity is the number of T-shirts that are ordered, what is the dependent quantity? Dependent quantity:

12 Directions: Determine the independent and dependent quantities in each scenario. 5. On her way to work each morning, Sophia purchases a small cup of coffee for $4.25 from the coffee shop. She wants to graph her weekly spending on coffee. What would be the independent and dependent quantities? Independent quantity: Dependent quantity: 6. Phillip enjoys rock climbing on the weekends. At some of the less challenging locations he can climb upwards of 12 feet per minute. Choosing between distance and time, what would be the independent and dependent quantities? Independent quantity: Dependent quantity: 7. Gavin works for a skydiving company. Customers pay $200 per jump to skydive in tandem skydives with Gavin. Using the amount of money made and number of jumps, what would be the independent and dependent quantities? Independent quantity: Dependent quantity: 8. Gillian is playing video games at an arcade. Gillian starts with $40 and is playing games that cost 50 cents per game. The amount of money in his pocket can be figured at any time, by just knowing how many games he has played. Independent quantity: Dependent quantity: 9. Julian works as a salesman for a textbook company. He only receives income based on a 10% commission on the amount of sales. What would be the independent and dependent quantities? Independent quantity: Dependent quantity: 10. A freshly made cup of tea is served at a temperature of about 180 F. The tea cools rapidly at first, and then slows down gradually as it approaches room temperature. Independent quantity: Dependent quantity: 11. Brady runs for his high school cross country team. His strategy for each 5-kilometer race is always the same. He starts off at a medium pace and gradually increases his speed the closer he is to the finish. Independent quantity: Dependent quantity:

13 Name: Date: Period: Worksheet 6 Directions: Choose the graph that best models each scenario. 1. Lyndsay is filling her pool to get ready for summer. She is using her hose to fill the pool at a rate of 14 gallons per minute. 2. Isaiah is training to participate in competitive trampoline. In his best jump, he can reach a maximum height of about 9 meters and can spend about 2 seconds in the air performing tricks. 3. Each day Jasmine starts her walk to school at 7:45am. At 7:50am she stops at her friend Victoria s house. Victoria is usually late and Jasmine must wait at least 5 minutes while her friend gets ready. At 7:55am the girls leave the house and arrive at school at 8:10am.

14 4. Jasmine is saving for college. She has invested $500 in a mutual fund that is expected to earn an average of 7% annually. 5. Marcus is at the top of an observation tower. He drops an action figure with a parachute attached and watches it descend to the ground. 6. Janelle holds a raffle to raise money for a children s hospital. Participants who enter the raffle guess the number of peanuts in a jar. Janelle records the number of peanuts each participant guesses and the number of peanuts their guess is off by.

15 Directions: Label the axes of the graph that models each scenario with the independent and dependent quantities. 7. Madison enjoys bicycling for exercise. Each Saturday she bikes a course she has mapped out around her town. She averages a speed of 12 miles per hour on her journey. 8. Natasha is filling the bathtub with water in order to give her dog Buster a bath. The faucet fills the tub at an average rate of 12 gallons per minute. 9. Marcus throws a football straight up into the air. After it reaches its maximum height of 20 feet, it descends back to the ground.

16 10. Chloe is using a pump to drain her backyard pool to get ready for winter. The pump removes the water at an average rate of 15 gallons per minute. 11. Jermaine is saving money to purchase a used car. He places $850 dollars in a savings account that earns 1.65% interest annually. 12. Zachary enjoys hiking. On the first day of his latest hiking trip, he hikes through flat terrain for about 8 miles. On the second day, he hikes through very steep terrain for about 3 miles. On the third day he hikes through some hilly terrain for about 6 miles.

17 Name: Date: Period: Worksheet Review Directions: Answer each of the following questions. 1. Hector knows there is a relationship between the number of cars he washes and the time it takes him to wash those cars. Identify the independent quantity and the dependent quantity in the problem situation. 2. David rode his bike to the park. After staying at the park for a few minutes, he then continued his ride to the grocery store. The graph shows this relationship. In the graph, what is the independent quantity and what is the dependent quantity? 3. Tell whether each graph represents a function. a. b. 4. Classify each function as increasing, decreasing, or constant. a. ff(xx) = 3xx b. ff(xx) = 2 xx, where x is an integer c. ff(xx) = 0.9 xx d. ff(xx) = 9 5. Classify each function as a linear function, a linear absolute value function, a quadratic function, or an exponential function. a. ff(xx) = 7xx b. ff(xx) = 3xx 2 c. ff(xx) = 4 xx d. ff(xx) = 8

18 6. Determine whether each function has an absolute maximum or absolute minimum. If the graph has neither an absolute maximum or absolute minimum, write none. a. ff(xx) = 4 xx b. ff(xx) = 2xx + 5 c. ff(xx) = 5xx d. ff(xx) = 3 xx 7. Create an equation and sketch a graph for each set of given characteristics. a. is a function b. is a function is quadratic is a linear absolute value function is continuous is discrete has an absolute minimum has an absolute maximum 8. Sam rode in a hot air balloon. After the balloon began its initial descent, it stayed in the air at a constant height for a few minutes, and then it continued its descent to the ground. The graph shows this relationship. In the graph, what is the independent quantity and what is the dependent quantity? Sam s Hot Air Balloon Ride

19 9. Angela knows there is a relationship between the area of the squares she draws and the side length of each square. Identify the independent quantity and the dependent quantity in the problem situation. 10. Over which part of the domain is the function constant? The amazing Stevini is practicing one of his tricks. As part of this trick, he cuts a rope into many pieces and then magically puts the pieces back together. He begins the trick with a 20 foot rope and then cuts in half. He then takes one of the halves and cuts that piece in half. He repeats this process until he left with a piece so small he can no longer cut it. a. What would be an appropriate function family for this function? Explain your reasoning. b. Is the function continuous or discrete? Explain why in terms of the scenario. c. In the context of the scenario, what is causing the graph to be a decreasing function?

20 12. Joe is mowing lawns to buy a new car. For every lawn that he mows he earns $50. a. Identify the dependent quantity b. Identify the independent quantity c. Sketch the graph of the scenario. d. Label the x and y axis, include unit of measurement. e. Label the approximate scale of the graph.