4-1. Using Graphs to Relate Two Quantities. Vocabulary. Review. Vocabulary Builder. Use Your Vocabulary

Transcription

1 - Using Graphs to Relate Two Quantities Vocabular Review Use the graph at the right. Draw a line from each point in Column A to its coordinates in Column B. Column A Column B L. point K (, ). point L (, ). point M (, ). point N (, ) 5. point P (, ) P K N O M Vocabular Builder analze (verb) AN uh lz Other Word Forms: analzed (verb), analsis (noun) Definition: to eamine carefull in detail; to identif the nature and relationship of its parts What It Means: break down, dissect Word Origin: from the Greek word analusis, meaning a dissolving Use Your Vocabular Complete each statement with the appropriate word from the list. analze analsis analzed 6. The chemist 9 the data to draw a conclusion. 7. Jean needed to 9 the data she gathered in her eperiment. 8. An 9 of the traffic at an intersection showed the need for a traffic light. analzed analze analsis Chapter

2 Problem Analzing a Graph Got It? What are the variables in the graph? Describe how the variables are related at various points on the graph. Board Length Length Time 9. Circle the two variables being related in the graph. time cut board length. Show how the variables are related b underlining the correct word or words to complete each sentence. The length of the board increases / decreases with time. The length of the board is constant / decreasing while ou are actuall cutting the board. During the time shown on the graph, there are three / four cuts. There is / is not a piece of the board left at the end of the time shown. Got It? What are the variables in the graph? Describe how the variables are related at various points on the graph.. Show how the variables are related b underlining the correct word to complete each sentence. The cost of the cell phone in June increases / decreases with number of minutes of calls. The cost of the cell phone in June is constant / increasing for the first part of the month.. Use our answers from Eercise to describe how the variables in the graph are related. Answers ma var. Sample: For the first part of the month of June, the cost of the cell phone remains constant. Then the cost increases steadil for the rest of the month as the number of minutes of calls increases. Cost June Cell Phone Cost Minutes of Calls Lesson -

3 Problem Matching a Table and a Graph Got It? The table shows the amount of sunscreen left in a can based on the number of times the sunscreen has been used. Which graph could represent the data shown in the table? Sunscreen Number of Uses Amount of Sunscreen (oz) A. Amount of Sunscreen Number of Uses B. Amount of Sunscreen Number of Uses C. Amount of Sunscreen Number of Uses. Analze the data in the table. Complete each statement with the correct choice from the list. Use each word onl once. slowl fall decreases The amount of sunscreen in the container 9 after each use. The amount of sunscreen in the container changes 9. The graph should 9 at a slow rate. decreases slowl fall. The graph that could represent the data shown in the table is Graph C. Problem Height Sketching a Graph Got It? Suppose ou start to swing ourself on a plaground swing. You move back and forth and swing higher in the air. Then ou slowl swing to a stop. What sketch of a graph could represent how our height from the ground might change over time? Label each section. 5. Multiple Choice The two variables being related are time and 9. length of distance from our height our height swing top of swing from ground 6. Consider the three ccles during the middle of our time on the swing. Circle the best sketch of our height from the ground during that time. constant distance start high, swing low, start low, swing from ground end high high, end low Height Height Time Time Time Chapter

4 Lesson Check Do ou UNDERSTAND? Reasoning Describe a real-world relationship that could be represented b the graph sketched at the right. 7. Draw a line from the name of each segment in Column A to its verbal description in Column B. A B C D E Column A A B C D E Column B spilling water from a cup pouring water into a cup quickl stop pouring water into a cup water leaking from a hole in a cup pouring water into a cup slowl 8. Use the verbal descriptions above to help ou write a situation that could be represented b the sketch. Answers ma var. Sample: At first I poured water quickl into a cup, but then I slowed down. I stopped pouring because I saw the cup wobble. It fell over and much of the water spilled out. The remaining water leaked out slowl from a hole in the cup. Math Success Check off the vocabular words that ou understand. variable quantities increase decrease Rate how well ou can use graphs. Need to review 6 8 Now I get it! Lesson -

5 - Patterns and Linear Functions Vocabular Review. A function is a relationship that pairs each input value with eactl one output value. Cross out the relationship below that does NOT show a function. Input 5 Output Input Output Input Output Vocabular Builder independent (adjective) in dee PEN dunt Related Words: dependent, input, output Definition: An independent variable is a variable whose value determines the value of another variable, called the dependent variable. Math Usage: In the diagram, the independent variable,, is called the input of the function. The dependent variable,, is called the output of the function. Eample: When showing the relationship between amount of sunlight and amount of plant growth, the independent variable is the amount of sunlight. Use Your Vocabular Write I if the first value is independent of the second value. Write D if the first value is dependent on the second value. D I D. the growth of a plant and the light the plant receives. the speed of a swimmer and the depth of a pool. the number of books a shelf holds and the length of the shelf independent variable (input) function dependent variable (output) Chapter

6 Problem Representing a Geometric Relationship Got It? In the diagram below, what is the relationship between the number of triangles and the perimeter of the figure the form? Represent this relationship using a table, words, an equation, and a graph. triangle triangles triangles triangles 5. Define the variables. Let 5 the number of triangles. Let 5 the perimeter of the figure. 6. Complete the table. Number of Triangles Perimeter 8 7. Complete the model below. Relate perimeter is times number of triangles plus 6 Write = Write an equation to represent the relationship ou wrote in Eercise Use the table to list the points ou will plot. (, ) (, ) (, 8 ) (, ). Now plot the points on the graph. 8 Perimeter Number of Triangles 5 Lesson -

7 Problem Representing a Linear Function Got It? Is the relationship in the table at the right a linear function? Describe the relationship using words, an equation, and a graph. Input, Output, 8. Describe the pattern in the table in words. The value of is equal to the sum of times and 8.. Multiple Choice Which equation describes the relationship in the table? Plot the points from the table on the graph Underline the correct word or words to complete the sentence. The points lie / do not lie on a line; so, the relationship is / is not a linear function. Got It? Reasoning Does the set of ordered pairs (, ), (, ), (, 5), and (, 8) represent a linear function? Eplain. 5. Plot the points on the graph Do the ordered pairs represent a linear function? Eplain. No. Eplanations ma var. Sample: The input value has two output values, and 8. The points do not all lie on a line. Chapter 6

8 Lesson Check Do ou UNDERSTAND? Vocabular The amount of toothpaste in a tube decreases each time ou brush our teeth. Identif the independent and dependent variables in this relationship. 7. Complete each phrase to identif the variables. Let A 5 the amount of toothpaste in a 9. Let B 5 the number of times ou 9 our teeth. tube brush 8. Underline the correct word to complete each sentence. A is the independent / dependent variable. B is the independent / dependent variable. Lesson Check Do ou UNDERSTAND? Reasoning Does the graph at the right represent a linear function? Eplain. 9. Draw a line from each word in Column A to its definition in Column B. Column A Column B relation function whose graph is a line or part of a line function pairing of input and output values linear function O relationship that pairs each input value with eactl one output value. Use the terms above to eplain whether or not the graph represents a linear function. The graph does not represent a linear function. Eplanations ma var. Sample: There is onl one output for ever input, so the graph represents a function. It is not a linear function because the graph is curved, not part of a line. Math Success Check off the vocabular words that ou understand. dependent variable independent variable linear function Rate how well ou can describe linear functions. Need to review 6 8 Now I get it! 7 Lesson -

9 - Patterns and Nonlinear Functions Vocabular Review Find the net number in each pattern..,,, 8, 6. 8,,,.,, 9, 7, 8.,, 8, 6 5. The net shape in the pattern below has 6 blocks. Vocabular Builder nonlinear (adjective) nahn LIN ee ur Related Words: line (noun), linear (adjective) Definition: Something that is nonlinear is not in a straight line. Math Usage: A nonlinear function is a function whose graph is not a line or part of a line. A linear function is a function whose graph is a line or part of a line. Common Usage: A nonlinear narrative is a stor where the events are told out of chronological order. Use Your Vocabular 6. Circle each graph of a nonlinear function. O O O O Chapter 8

10 Problem Classifing Functions as Linear or Nonlinear Got It? The table below shows the fraction A of the original area of a piece of paper that remains after the paper has been cut in half n times. Graph the function represented b the table. Is the function linear or nonlinear? Cutting Paper Number of Cuts, n Fraction of Original Area Remaining, A Complete each ordered pair. (, ) (, ) (, 8 ) (, 6 ) 8. Graph the ordered pairs from Eercise 7 on the coordinate plane. Fraction of Area Remaining A 5 Number of Cuts n 9. Complete the sentence with linear or nonlinear: The function is 9. Got It? Reasoning Will the area A in Eercise 8 ever reach zero? Eplain.. If ou start with a piece of paper in our hand and repeatedl cut the paper in half, will our hand ever be empt?. Will the remaining area A ever reach zero? Eplain. Yes / No nonlinear No. Eplanations ma var. Sample: Each time ou cut the paper in half, the remaining area gets closer to zero, but will never disappear entirel. 9 Lesson -

11 Problem Representing Patterns and Nonlinear Functions Got It? The table shows the number of new branches in each figure of the pattern below. What is a pattern ou can use to complete the table? Represent the relationship using words, an equation, and a graph. Number of Figure, 5 Number of New Branches, 9 7. Look for a pattern in the table. Describe it below. Answers ma var. Sample: The number of new branches in each figure is times the number of new branches in the previous figure.. Use the words the figure and new branches to complete the diagram below. the number of new branches the number of the figure. Circle the equation that represents the function Complete each statement. When 5, 5 8. When 5 5, Write ordered pairs to represent the data in the table and our results from Eercise 5. Then graph the data. (, ) (, 9) (, 7) (, 8 ) (5, ) You can think of a function as a rule that ou appl to the input in order to get the output. You can describe a nonlinear function with words or with an equation, just as ou did with linear functions. Problem Number of New Branches 5 5 Writing a Rule to Describe a Nonlinear Function Got It? What is a rule for the function represented b the ordered pairs (, ), (, ), (, 9), (, 6), and (5, 5)? 5 5 Figure Number Chapter

12 7. Make a table to organize the - and -values Use words to eplain the relationship between the - and -values. Eplanations ma var. Sample: The -value is found b squaring the -value. 9. Now use the relationship ou described to write an equation that is a rule for the function. 5 Lesson Check Do ou UNDERSTAND? Error Analsis A classmate sas that the function in the table at the right can be represented b the rule 5. Describe and correct our classmate's error.. Use the ordered pairs below. Cross out the ordered pairs that are NOT described b the equation 5. (, ) (, ) (, 5) (, ) (, 7). Eplain our classmate s error in using 5 to describe the function. 5 7 Eplanations ma var. Sample: M classmate chose a rule that describes onl two points in the table. The rule must describe all of the points.. Circle the equation that correctl describes the function. Math Success Need to review Check off the vocabular words that ou understand. linear function nonlinear function Rate how well ou can describe nonlinear functions. 6 8 Now I get it! Lesson -

13 - Graphing a Function Rule Vocabular Review Find each input or output.... Write T for true or F for false. 7 T. The inputs of a function are the domain of the function. T 5. A function pairs ever input with eactl one output. Vocabular Builder discrete (adjective) dih SKREET Related Words: separate (adjective), distinct (adjective) Main Idea: Discrete describes something consisting of distinct or unconnected elements. Eample: The set of integers is a discrete set. Noneample: The set of real numbers is not a discrete set. Use Your Vocabular 6. Circle the word or words that mean the opposite of discrete. separate continuous infinite countable 7. Circle the situation below that describes a discrete set. the possible temperatures in Florida the number of oranges sold at a fruit stand each da Chapter

14 Problem Graphing a Function Rule Got It? What is the graph of the function rule 5? 8. Complete the table below. Then graph each ordered pair on the coordinate plane at the right. Connect the points with a line. (, ).5 (,.5) (, ) O.5 (,.5) (, ) When ou graph a real-world function rule, choose appropriate intervals for the units on the aes. Ever interval on an ais should represent the same change in value. If all the data are nonnegative, show onl the first quadrant. Problem Graphing a Real-World Function Rule Got It? The function rule W 5 8g 7 represents the total weight W, in pounds, of a spa that contains g gallons of water. What is a reasonable graph of the function rule given that the capacit of the spa is 5 gal? 9. Use the values of g to complete the table. g W 8g 7 W 8(5) 7 W 8(5) 7 9 W 8(5) 7 7 (g, W) W 8() 7 7 (, 7) (5, ) (5, 9) (5, 7). Graph the ordered pairs on the coordinate plane at the right. Connect the points with a line segment. Total Weight W Spa Weight Gallons of Water g Lesson -

15 Ke Concept Continuous and Discrete Graphs A continuous graph is a graph that is unbroken. Label each graph as discrete or continuous.. A discrete graph is a graph composed of distinct, isolated points.. O O continuous discrete Problem Identifing Continuous and Discrete Graphs Got It? The amount of water w in a wading pool, in gallons, depends on the amount of time t, in minutes, the wading pool has been filling, as related b the function rule w 5 t. Graph the function rule. Is the graph continuous or discrete? Justif our answer.. Complete the table to find each value of w.. Graph each ordered pair on the coordinate plane. t w Underline the correct word or words to complete each sentence. While the pool is filling, the water will / will not enter throughout a given minute. The points on the graph should / should not be connected b a line. The graph is continuous / discrete. Problem Graphing Nonlinear Function Rules Got It? What is the graph of the function rule 5? 6. Cross out an ordered pair that does not lie on the graph of 5. Water (gallons) Water in Wading Pool Time (minutes) (, 9) (, ) (, ) (, ) (, 9) Chapter

16 7. Circle the letter of the correct graph of the function Lesson Check Do ou UNDERSTAND? Error Analsis Your friend graphs 5 at the right. Describe and correct our friend's error. 8. Circle the name for the -values our friend used. integers rational numbers real numbers whole numbers 9. Circle the best name for the -values of 5. O integers rational numbers real numbers whole numbers. Describe our friend s error. Eplanations ma var. Sample: The graph should be a line, since noninteger values of satisf the function.. Graph the function correctl on the coordinate plane at the right. Math Success Check off the vocabular words that ou understand. continuous graph Rate how well ou can graph function rules. discrete graph 5 5 O 5 5 Need to review 6 8 Now I get it! 5 Lesson -

17 -5 Writing a Function Rule Vocabular Review In function notation, ou read f() as f of. You can think of the value f() as another wa of writing.. Write how ou would read h(g) aloud. h of g. Circle the equation that shows function notation. f() 5 5 f f().8. Carmine wants to bu some peaches. Each peach costs $.5. Circle the function Carmine could use to find the cost of an number of peaches p..5c 5 p(c) c(p) 5.5 c(p) 5.5p.5 5 c? p(c) Vocabular Builder rule (noun) rool Main Idea: A mathematical rule is a method or procedure that describes how to solve a problem. Eample: A rule of integer multiplication is that a negative integer multiplied b a negative integer produces a positive integer. Use Your Vocabular Consider the rule a b c d 5 a b? d c, for b, c, d u.. Circle the equation that is an eample of this rule. 5 5? 5 5 5? 5. According to this rule, 6 9 5? Circle the correct words to complete the sentence. The reason that this rule states that b, c, d is because ? ou cannot multipl b ou cannot divide b the dividend cannot be Chapter 6

18 Problem Writing a Function Rule Got It? A landfill has 5, tons of waste in it. Each month it accumulates an average of more tons of waste. What is a function rule that represents the total amount of waste after m months? 7. Complete the model below. Relate total waste is 5, tons of waste plus tons of waste each month times number of months Define Let T the total waste, and let m the number of months. Write T 5, m 8. Write an equation to represent the situation. T 5 5, m Problem Writing and Evaluating a Function Rule Got It? A kennel charges $5 per da to board dogs. Upon arrival, each dog must have a flea bath that costs $. Write a function rule for the total cost for n das of boarding plus a bath. How much does a -da sta cost? 9. Define our variables. Let T 5 total cost. Let n 5 number of das.. Now complete the reasoning model below. Think I will have to pa $5 per da to board m dog. How much will that cost for n das? I also have to pa $ for the flea bath. If I put those together, I can write a formula for the total cost, T.. Now evaluate T for n 5. T 5 5n T 5 5? T 5 5 T T 5 Write n n. The cost of a -da sta is $ 6. 7 Lesson -5

19 Problem Writing a Nonlinear Function Rule Got It? Write a function rule for the area of a triangle whose height is in. more than twice the length of its base. What is the area of the triangle when the length of its base is 6 in.?. Use the given information to write an equation for the height of the triangle. Let h 5 the height of the triangle. Let b 5 the length of the base of the triangle. Relate h in. more than twice the length of its base Write h b. Use the justifications at the right to find a function rule for the area of the triangle. A 5? b? h Formula for area of a triangle A 5? b? (b ) Substitute for h. A 5? b? b Distribute b. A 5 b b Simplif. 5. Now find the area of the triangle when its base is 6 in. A 5 6? 6 Substitute 6 for b. A 5 56 Evaluate the eponent and the multiplication. A 5 88 Add. 6. The area of the triangle is 88 in. Got It? Reasoning Graph the function rule from Eercise. How do ou know the rule is nonlinear? 7. Complete the table of values. b 7 A b 7 7 b A 6 Chapter 8

20 8. Graph the ordered pairs (b, A) that ou found in Eercise 7. Use the points to graph the function rule. 9 A 6 9. How do ou know the rule is nonlinear? Eplain. 6 8 b Eplanations ma var. Sample: The graph of the function is curved, which means the function is nonlinear. Lesson Check Do ou UNDERSTAND? Reasoning Is the graph of a function rule that relates a square s area to its side length continuous or discrete? Eplain.. Underline the correct word to complete each sentence. A continuous / discrete graph is unbroken. A continuous / discrete graph is composed of isolated points. The number of possible values for the length of a side of a square is finite / infinite.. Is the graph continuous or discrete? Eplain. The graph is continuous. Eplanations ma var. Sample: The length of a side of a square can be an nonnegative value. The graph includes all values between the whole numbers. Math Success Check off the vocabular words that ou understand. function notation Rate how well ou can write function rules. Need to review function rule 6 8 Now I get it! 9 Lesson -5

21 -6 Formalizing Relations and Functions Vocabular Review. Use the words below to label the function machine at the right. Use each word once. function rule -values output -values input range domain input -values equation function rule range -values output -values Vocabular Builder reasonable (adjective) ree zun uh bul Definition: Something is reasonable if it makes sense or is sensible. Eample: It is reasonable to epect warm weather in Miami in Jul. Noneample: It is not reasonable to epect snow in Miami in Jul. Other Word Forms: reasonableness (noun); reasonabl (adverb) Opposite: unreasonable (adjective) Use Your Vocabular Complete each sentence with the appropriate word from the list. reasonable reasonableness unreasonable. The student estimated to check the 9 of her answer.. Sales ta of $ on an $85 item is 9.. A price of $ is 9 for a pizza. reasonableness unreasonable reasonable Chapter

22 Problem Identifing Functions Using Mapping Diagrams Got It? Identif the domain and range of the following relation: {(.,.5), (5,.), (7,.8), (., )} Represent the relation with a mapping diagram. Is the relation a function? 5. Use the words domain and range to label the mapping diagram. Then draw arrows to represent the relation. domain. 5 7 range Does the relation map each domain value to eactl one range value? Yes / No 7. Is the relation a function? Yes / No You can use the vertical line test to decide whether a relation is a function. If an vertical line passes through more than one point of the graph, then the relation is not a function. Problem Identifing Functions Using the Vertical Line Test Got It? Is the relation {(, ), (, ), (, ), (, ), (, )} a function? Use the vertical line test. 8. Begin b graphing the points from the relation on the coordinate plane. O 9. Can ou draw a vertical line that intersects more than one point? If so, draw it. Yes / No. Is the relation a function? Yes / No Lesson -6

23 Problem Evaluating a Function Got It? The function w() 5 5 represents the number of words w() ou can read in minutes. How man words can ou read in 6 min?. You should substitute 6 for.. The function is evaluated below. Write the justification for each step. w() 5 5 w(6) 5 5? 6 w(6) 5 5 Write the original function. Substitute 6 for. Multipl.. You can read 5 words in 6 minutes. Problem Finding the Range of a Function Got It? The domain of g() 5 is {,, 5, 7}. What is the range?. Underline the correct word to complete each sentence. The domain / range is the set of input values. The domain / range is the set of output values. 5. Use the function g() 5 with domain {,, 5, 7}. Find each output. g() g() g() 5 () 5 58 g(5) g(5) 5 (5) Problem 5 g(7) 6. The range of g() 5 with domain {,, 5, 7} is { 8,, 8, 6 }. g() 5 () 5 5 g(7) 5 (7) Identifing a Reasonable Domain and Range Got It? You have 7 qt of paint to paint the trim in our house. A quart of paint covers ft. The function A(q) 5 q represents the area A(q), in square feet, that q quarts of paint cover. What domain and range are reasonable for the function? Chapter

24 7. Complete the reasoning model below. Think The least amount of paint I can use is qt. So, that is the least domain value. Write A( ) A( ) The greatest amount of paint I can use is 7 qt. So, that is the greatest domain value. A( 7 ) 7 A( 7 ) 7 8. A reasonable domain is # q # A reasonable range is # A(q) # 7. Lesson Check Do ou UNDERSTAND? Error Analsis A student drew the dashed line on the graph shown and concluded that the graph represented a function. Is the student correct? Eplain.. Describe how the vertical line test helps ou decide whether a relation is a function. Answers ma var. Sample: I know that if an vertical line passes through more than one O point of a graph, the relation is not a function.. Underline the correct word or words to complete each sentence about the graph. I can draw a vertical line that passes through onl one point / more than one point. Therefore the graph does / does not represent a function.. Describe the student s error. Answers ma var. Sample: The student drew one vertical line, but did not check other places on the graph where a vertical line might pass through more than one point. Math Success Check off the vocabular words that ou understand. relation domain range vertical line test function notation Rate how well ou understand functions. Need to review 6 8 Now I get it! Lesson -6

25 -7 Sequences and Functions Vocabular Review. Circle the name of the net shape in the pattern at the right. rectangle circle heagon octagon... Find the net number in each pattern..,, 9, 7. 6,,,,.,, 5, 5, 5 Vocabular Builder sequence (noun) SEE kwuns Fibonacci sequence,,,,, 5, 8,,,... Definition: A sequence is an ordered list of numbers that often form a pattern. Each number in the list is called a term of the sequence. Eample: The Fibonacci sequence is a sequence of numbers where the first number is, the second number is, and each subsequent number is equal to the sum of the previous two numbers. Origin: from the Latin word sequentia, which means to follow Use Your Vocabular The following sets of numbers are sequences. Eplain each pattern. 5. set of whole numbers greater than or equal to 5: {5, 6, 7, 8, 9, } Answers ma var. Sample: Beginning with 5, each whole number is more than the whole number before it. 6. {,,, 6, 8, } Answers ma var. Sample: Beginning with, each number is more than the number before it. Chapter

26 Problem Etending Sequences Got It? Describe a pattern in the sequence 5,, 7,,. What are the net two terms of the sequence? 7. Complete the diagram. What number is added to each term? Describe the pattern in the sequence. Answers ma var. Sample: Add 6 to each term to find the net term. _ 9. Find the net two terms in the sequence. 5,, 7,, 9, 5,... Problem Identifing an Arithmetic Sequence Got It? Tell whether the sequence 8, 5,,, is arithmetic. If it is, what is the common difference?. Complete the table. Consecutive Terms 8 and 5 5 and and Difference Do the consecutive terms have a common difference? Yes / No. Is the sequence an arithmetic sequence? If so, what is the common difference? _ No, the sequence is not arithmetic. The difference between terms is _ not the same. Got It? Tell whether the sequence 7, 9,,, is arithmetic. If it is, what is the common difference?. Complete the table. Consecutive Terms 7 and 9 9 and and Difference. Is the sequence an arithmetic sequence? If so, what is the common difference? _ Yes, the sequence is arithmetic. The difference between terms is. 5 Lesson -7

27 Ke Concept Rule for an Arithmetic Sequence The nth term of an arithmetic sequence with the first term A() and common difference d is given b this rule: A(n) A() (n )d nth term first term term c number c c a common difference 7. The equation A(5) 5 (5 )7 generates the fifth term in a sequence. Draw a line from each number in Column A to its description in Column B. Column A Column B 7 first term of the sequence 5 term number common difference Problem Writing a Recursive Formula Got It? Write the recursive formula for the arithmetic sequence, 9, 5,, What is the 9th term in the sequence? 8. A() = A() 5 A() A() 5 A() A() 5 A() The recursive formula for the arithmetic sequence is A(n) =. A(5) 5 A() A(6) 5 A(5) A(7) 5 A(6) A(8) 5 A(7) A(9) 5 A(8) Problem Writing an Eplicit Formula Got It? A subwa pass has a starting value of $. After one ride, the value of the pass is $98.5. After two rides, its value is $96.5. After three rides, its value is $9.75. Write a rule to represent the remaining value on the card as an arithmetic sequence. What is the value of the pass after 5 rides?. Describe how the values for A(n) are found A(n ) 6 Answers ma var. Sample: For each term, ou subtract another.75 because each time ou ride the _ subwa, it reduces the value of our pass b.75. _ Chapter 6

28 . How man times is.75 subtracted from when n 5? What is the A() term? a. How man times is.75 subtracted from when n 5? What is the A() term? 98.5 b. How man times is.75 subtracted from when n 5? 96.5 What is the A() term? c. How man times is.75 subtracted from when n 5? 9.75 What is the A() term? n d. How man times is.75 subtracted from when n 5 n? (n ).75 What is the A(n) term? 6 Using the formula, what is the value of the pass. What is n for the term after 5 rides are used? 7.75 after 5 rides? Lesson Check Do ou UNDERSTAND? Reasoning Can ou use the rule below to find the nth term of an arithmetic sequence with a first term A() and a common difference d? Eplain. A(n) 5 A() nd d. Use the Distributive Propert to write an equivalent formula. A(n) 5 A() d? (n ) A(n) 5 A() nd d 5. Can ou use the rule A(n) 5 A() nd d to find the nth term of an arithmetic sequence? Eplain. Yes. Eplanations ma var. Sample: Using the Distributive Propert, _ d(n ) 5 dn d. Since dn d 5 nd d, the formulas are the same. _ The are just written differentl. _ Math Success Check off the vocabular words that ou understand. sequence term of a sequence arithmetic sequence common difference Rate how well ou can understand arithmetic sequences. Need to review 6 8 Now I get it! 7 Lesson -7