A Picture Is Worth a Thousand Words

Transcription

1 Lesson 1.1 Skills Practice 1 Name Date A Picture Is Worth a Thousand Words Understanding Quantities and Their Relationships Vocabular Write a definition for each term in our own words. 1. independent quantit The quantit that the dependent quantit depends on is the independent quantit.. dependent quantit When one quantit depends on another in a problem situation, it is said to be the dependent quantit. Problem Set Determine the independent and dependent quantities in each scenario. 1. Selena is driving to visit her grandmother who lives 35 miles awa from Selena s home. She travels an average of miles per hour. Independent quantit: time (hours) Dependent quantit: distance (miles) 1 Carnegie Learning. Benjamin works at a printing compan. He is making T-shirts for a high school volleball team. The press he runs can imprint 3 T-shirts per minute with the school s mascot. Independent quantit: time (minutes) Dependent quantit: number of T-shirts imprinted 3. On her wa to work each morning, Sophia purchases a small cup of coffee for $.5 from the coffee shop. Independent quantit: number of cups Dependent quantit: cost (dollars) Chapter 1 Skills Practice 51

2 1 Lesson 1.1 Skills Practice page. Phillip enjos rock climbing on the weekends. At some of the less challenging locations he can climb upwards of 1 feet per minute. Independent quantit: time (minutes) Dependent quantit: distance climbed (feet) 5. Jose prefers to walk to work when the weather is nice. He walks the 1.5 miles to work at a speed of about 3 miles per hour. Independent quantit: time (hours) Dependent quantit: distance (miles). Gavin works for a skdiving compan. Customers pa $ per jump to skdive in tandem skdives with Gavin. Independent quantit: number of jumps Dependent quantit: cost (dollars) Choose the graph that best models each scenario. 7. Klie is filling her backard pool to get read for the summer. She is using a garden hose to fill the pool at a rate of 1 gallons per minute. Graph A Graph B Graph C Graph A. Hector is training to participate in competitive trampoline. In his best jump, he can reach a maimum height of about 9 meters and can spend about seconds in the air performing tricks. Graph A Graph B Graph C 1 Carnegie Learning Graph C 5 Chapter 1 Skills Practice

3 Lesson 1.1 Skills Practice page 3 1 Name Date 9. Jasmine is saving for college. She has invested $5 in a mutual fund that is epected to earn an average of 7% annuall. Graph A Graph B Graph C Graph B 1. Each da Maria starts her walk to school at 7:5 am. At 7:5 am she stops at her friend Jenna s house. Jenna is usuall late and Maria must wait at least 5 minutes for her to get read. At 7:55 am Maria and Jenna leave Jenna s house and arrive at school at :1 am. Graph A Graph B Graph C 1 Carnegie Learning Graph B Chapter 1 Skills Practice 53

4 1 Lesson 1.1 Skills Practice page 11. 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. Graph A Graph B Graph C Graph C 1. Janelle holds a raffle to raise mone 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 b. Graph A Graph B Graph C Graph A 1 Carnegie Learning 5 Chapter 1 Skills Practice

5 Lesson 1.1 Skills Practice page 5 1 Name Date Label the aes of the graph that models each scenario with the independent and dependent quantities. 13. Madison enjos biccling for eercise. Each Saturda she bikes a course she has mapped out around her town. She averages a speed of 1 miles per hour on her journe. Distance Madison Bikes Time (hours) 1 Carnegie Learning Distance (miles) 1. 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 1 gallons per minute. Amount of Water in Bathtub Volume (gallons) Time (minutes) Chapter 1 Skills Practice 55

6 1 Lesson 1.1 Skills Practice page 15. Marcus throws a football straight up into the air. After it reaches its maimum height of feet, it descends back to the ground. Football Height Height of Football (feet) Time (seconds) 1. Chloe is using a pump to drain her backard pool to get read for winter. The pump removes the water at an average rate of 15 gallons per minute. Amount of Water in Pool Volume (gallons) Time (minutes) 1 Carnegie Learning 5 Chapter 1 Skills Practice

7 Lesson 1.1 Skills Practice page 7 1 Name Date 17. Jermaine is saving mone to purchase a used car. He places $5 dollars in a savings account that earns 1.5% interest annuall. Interest Earned Interest (dollars) Time (ears) 1. Zachar enjos hiking. On the first da of his latest hiking trip, he hikes through flat terrain for about miles. On the second da, he hikes through ver steep terrain for about 3 miles. On the third da he hikes through some hill terrain for about miles. Distance Hiked 1 Carnegie Learning Distance (miles) Time (das) Chapter 1 Skills Practice 57

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9 Lesson 1. Skills Practice 1 Name Date A Sort of Sorts Analzing and Sorting Graphs Vocabular Match each definition to its corresponding term. 1. A graph with no breaks in it b. continuous graph a. discrete graph. The mapping between a set of inputs and a set of outputs c. relation b. continuous graph 3. The set of all input values of a relation e. domain c. relation. The set of all output values of a relation f. range d. function 5. A graph of isolated points a. discrete graph e. domain 1 Carnegie Learning. A visual method used to determine whether a relation represented as a graph is a function g. Vertical Line Test 7. A relation between a given set of elements for which each input value there eists eactl one output value d. function f. range g. Vertical Line Test Chapter 1 Skills Practice 59

10 1 Lesson 1. Skills Practice page Problem Set Each pair of graphs has been grouped together. Provide a rationale to eplain wh these graphs ma have been grouped together. 1. Graph A Graph B Answers will var. Both graphs are alwas decreasing from left to right. Both graphs are functions. Both graphs are made up of straight lines.. Graph A Graph B 1 Carnegie Learning Answers will var. Both graphs are smooth curves. Both graphs are functions. Both graphs have an increasing and a decreasing interval. Both graphs are U-shaped. Chapter 1 Skills Practice

11 Lesson 1. Skills Practice page 3 1 Name Date 3. Graph A Graph B Answers will var. Both graphs have an increasing and a decreasing interval. Both graphs have a minimum value. Both graphs are functions.. Graph A Graph B 1 Carnegie Learning Answers will var. Both graphs have discrete data values. Both graphs are decreasing from left to right. Both graphs are functions. Chapter 1 Skills Practice 1

12 1 Lesson 1. Skills Practice page 5. Graph A Graph B Answers will var. Both graphs are increasing from left to right. Both graphs are functions.. Graph A Graph B Answers will var. Both graphs have an increasing and a decreasing interval. Both graphs have a maimum value. Both graphs are functions. 1 Carnegie Learning Chapter 1 Skills Practice

13 Lesson 1. Skills Practice page 5 1 Name Date Determine whether the graph is discrete or continuous The graph is discrete. The graph is continuous. The graph is continuous Carnegie Learning The graph is continuous. The graph is discrete. The graph is continuous. Chapter 1 Skills Practice 3

14 1 Lesson 1. Skills Practice page Determine if each graph represents a function b using the Vertical Line Test Yes. The graph is a function. No. The graph is not a function No. The graph is not a function. Yes. The graph is a function. 1 Carnegie Learning Chapter 1 Skills Practice

15 Lesson 1. Skills Practice page 7 1 Name Date No. The graph is not a function. Yes. The graph is a function. 1 Carnegie Learning Chapter 1 Skills Practice 5

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17 Lesson 1.3 Skills Practice 1 Name Date There Are Man Was to Represent Functions Recognizing Algebraic and Graphical Representations of Functions Vocabular Choose the term from the bo that best completes each statement. function notation increasing function eponential functions function famil linear functions linear absolute value functions absolute maimum quadratic functions constant function linear piecewise functions decreasing function absolute minimum 1. Function notation is a wa to represent equations algebraicall that makes it more efficient to recognize the independent and dependent variables.. The famil of eponential functions includes functions of the form f() 5 a? b, where a and b are real numbers, and b is greater than but is not equal to The famil of linear piecewise functions includes functions that have an equation that changes for different parts, or pieces, of the domain.. When both the independent and dependent variables of a function increase across the entire domain, the function is called an increasing function. 5. A function has an absolute maimum if there is a point on its graph that has a -coordinate that is greater than the -coordinates of ever other point on the graph.. A function famil is a group of functions that share certain characteristics. 7. The famil of linear absolute value functions includes functions of the form f() 5 a 1 b 1 c, where a, b, and c are real numbers, and a is not equal to. 1 Carnegie Learning. When the dependent variable of a function decreases as the independent variable increases across the entire domain, the function is called a decreasing function. 9. The famil of quadratic functions includes functions of the form f() 5 a 1 b 1 c, where a, b, and c are real numbers, and a is not equal to. 1. The famil of linear functions includes functions of the form f() 5 a 1 b, where a and b are real numbers, and a is not equal to. 11. If the dependent variable of a function does not change or remains constant over the entire domain, then the function is called a constant function. 1. A function has an absolute minimum if there is a point on its graph that has a -coordinate that is less than the -coordinates of ever other point on the graph. Chapter 1 Skills Practice 7

18 1 Lesson 1.3 Skills Practice page Problem Set Rewrite each function using function notation. 1. Rewrite the function 5 3 using function notation so that the dependent quantit, defined as f, is a function of the independent quantit. f() 5 3. Rewrite the function using function notation so that the dependent quantit, defined as C, is a function of the independent quantit. C() Rewrite the function using function notation so that the dependent quantit, defined as P, is a function of the independent quantit. P() Rewrite the function l 5 n using function notation so that the dependent quantit, defined as L, is a function of the independent quantit n. L(n) 5 n 5. Rewrite the function d 5 1 m 1 5 using function notation so that the dependent quantit, defined as A, is a function 1 of the independent quantit m. A(m) 5 m 1 5. Rewrite the function c 5 p r using function notation so that the dependent quantit, defined as C, is a function of the independent quantit r. C(r) 5 p r 1 Carnegie Learning Chapter 1 Skills Practice

19 Lesson 1.3 Skills Practice page 3 1 Name Date Choose the graph that represents each function. Use our graphing calculator. 7. f() Graph A Graph B Graph C Graph A. f() 5 1 Graph A Graph B Graph C Graph C 1 Carnegie Learning 9. f() Graph A Graph B Graph C Graph B Chapter 1 Skills Practice 9

20 1 Lesson 1.3 Skills Practice page 1. f() 5 Graph A Graph B Graph C Graph C 11. f() 5, where is an integer Graph A Graph B Graph C Graph A 1. f() 5 Graph A Graph B Graph C 1 Carnegie Learning Graph B 7 Chapter 1 Skills Practice

21 Lesson 1.3 Skills Practice page 5 1 Name Date Determine whether each graph represents an increasing function, a decreasing function, a constant function, or a combination of increasing and decreasing functions The graph represents an The graph represents an The graph represents a increasing function. increasing function. function with a combination of an increasing interval and a decreasing interval Carnegie Learning The graph represents a The graph represents a The graph represents a decreasing function. constant function. decreasing function. Chapter 1 Skills Practice 71

22 1 Lesson 1.3 Skills Practice page Determine whether each graph represents a function with an absolute minimum, an absolute maimum, or neither The graph represents a The graph represents a The graph represents a function with an absolute function with neither an function with an absolute minimum. absolute minimum nor an maimum. absolute maimum The graph represents a The graph represents a The graph represents a function with neither an function with an absolute function with an absolute absolute minimum nor an maimum. minimum. absolute maimum. 1 Carnegie Learning 7 Chapter 1 Skills Practice

23 Lesson 1.3 Skills Practice page 7 1 Name Date Determine whether each graph represents a linear function, a quadratic function, an eponential function, a linear absolute value function, a linear piecewise function, or a constant function The graph represents an The graph represents a The graph represents a linear eponential function. linear function. piecewise function Carnegie Learning The graph represents a The graph represents a The graph represents a linear quadratic function. constant function. absolute value function. Chapter 1 Skills Practice 73

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25 Lesson 1. Skills Practice 1 Name Date Function Families for, Ale Recognizing Functions b Characteristics Problem Set Choose the appropriate function famil or families to complete each sentence based on the given characteristic(s). linear functions eponential functions quadratic functions linear absolute value functions 1. The graph of this function famil is a straight line. The function famil is linear functions.. The graph of this function famil has an increasing interval and a decreasing interval. The function famil is quadratic functions or linear absolute value functions. 3. The graph of this function famil has an absolute minimum. The function famil is quadratic functions or linear absolute value functions.. The graph of this function famil in decreasing over the entire domain. The function famil is linear functions or eponential functions. 5. The graph of this function famil forms a V shape. The function famil is linear absolute value functions.. The graph of this function famil has an increasing interval and a decreasing interval and forms a U shape. The function famil is quadratic functions. 1 Carnegie Learning 7. The graph of this function famil does not have an absolute maimum or absolute minimum and is a smooth curve. The function famil is eponential functions.. The graph of this function famil has an absolute maimum or absolute minimum and is made up straight lines. The function famil is linear absolute value functions. 9. The graph of this function famil is made up straight lines and does not have an absolute maimum or absolute minimum. The function famil is linear functions. 1. The graph of this function famil decreases over the entire domain and is a smooth curve. The function famil is eponential functions. Chapter 1 Skills Practice 75

26 1 Lesson 1. Skills Practice page Create an equation and sketch a graph for a function with each set of given characteristics. Use values that are an real numbers between 1 and Create an equation and sketch a graph that: is a smooth curve, is continuous, has a minimum, and is quadratic. Answers will var. f() 5 1. Create an equation and sketch a graph that: is linear, is discrete, and is decreasing across the entire domain. Answers will var. f() 5, where is an integer 1 Carnegie Learning 7 Chapter 1 Skills Practice

27 Lesson 1. Skills Practice page 3 1 Name Date 13. Create an equation and sketch a graph that: is a smooth curve, is increasing across the entire domain, is continuous, and is eponential. Answers will var. f() 5 1. Create an equation and sketch a graph that: has a maimum, is continuous, and is a linear absolute value function. 1 Carnegie Learning Answers will var. f() 5 Chapter 1 Skills Practice 77

28 1 Lesson 1. Skills Practice page 15. Create an equation and sketch a graph that: is linear, is continuous, is neither increasing nor decreasing across the entire domain, and does not pass through the origin. Answers will var. f() Create an equation and sketch a graph that: is discrete, has a maimum, does not pass through the origin, and is quadratic. Answers will var. f() 5 1 3, where is an integer 1 Carnegie Learning 7 Chapter 1 Skills Practice

29 Lesson 1. Skills Practice page 5 1 Name Date Choose the function famil represented b each graph. linear function quadratic function eponential function linear absolute value function linear piecewise function The graph represents a quadratic function. The graph represents a linear function Carnegie Learning The graph represents a linear absolute value function. The graph represents an eponential function. Chapter 1 Skills Practice 79

30 1 Lesson 1. Skills Practice page 1.. The graph represents a linear piecewise function. The graph represents a linear function. 1 Carnegie Learning Chapter 1 Skills Practice