(x, y) ( 1, 2) (0, 1) (1, 0) (2, 1)

Transcription

1 Date Dear Famil, In this chapter, our child will learn about patterns, functions, and graphs. Your child will learn that the same set of data can be represented in different was, including tables, equations, and graphs. Your child will also identif patterns in data, interpret sets of data, and use equations to represent relationships among sets of data. Your child will begin b graphing ordered pairs on a coordinate plane. Ordered Pairs (, 1) (, ) (1, 0) 1 ( 1, ) O (0, 1) 0 1 (0, 1) ( 1, ) 1 0 (1, 0) 1 (, 1) Net, our child will relate graphs to situations. He or she will read about situations and will identif or draw graphs that match these situations. For eample, this graph shows a situation in which the ink in a computer cartridge is completel used up. Then the cartridge is refilled, and the ink is used up again. Time Your child will then learn about functions and will graph them. A mathematical function is a rule that pairs one output value to each input value. For eample, the rule might be multipl a number b and then subtract 1 from the result. The equation that represents this function is 1, where is the input and is the output. You can use a table to organize input and output values and write ordered pairs which can be graphed. Input Rule Output Ordered Pair 1 (, ) 1 ( 1) 1 3 ( 1, 3) 0 (0) 1 1 (0, 1) Amount of Ink 6 6 O Holt Mathematics

2 The function is a linear function because its graph is a nonvertical line. A linear function describes an output that is changing at a constant rate. Your child will learn to use functions to solve problems involving constant rates of change, such as rising temperatures. Your child will also look for patterns in sequences. In an arithmetic sequence, the same number is added to each term to get the net term. Eample:, 7, 10, 13, 3 is added to each term. In a geometric sequence, each term is multiplied b the same number to get the net term. Eample:, 8, 3, 18, Each term is multiplied b. The terms of a sequence can be written as outputs () in a function table. Input values are represented b n, the number of each term. This table helps to write a function that describes the arithmetic sequence above. n Rule 1 3(1) 1 3() (3) () 1 13 The rule is to multipl n b 3 and add 1. The function is 3n 1. To find the 6th term in the sequence, substitute 6 for n in the function. 3n 1 3(6) 1 19 The 6th term is 19. For additional resources, visit go.hrw.com and enter the keword MS7 Parent. Holt Mathematics

3 Date Dear Famil, In this chapter, our child will learn about patterns, functions, and graphs. Your child will learn that the same set of data can be represented in different was, including tables, equations, and graphs. Your child will also identif patterns in data, interpret sets of data, and use equations to represent relationships among sets of data. Your child will begin b graphing ordered pairs on a coordinate plane. Ordered Pairs (, 1) (, ) (1, 0) 1 ( 1, ) O (0, 1) 0 1 (0, 1) ( 1, ) 1 0 (1, 0) 1 (, 1) Net, our child will relate graphs to situations. He or she will read about situations and will identif or draw graphs that match these situations. For eample, this graph shows a situation in which the ink in a computer cartridge is completel used up. Then the cartridge is refilled, and the ink is used up again. Time Your child will then learn about functions and will graph them. A mathematical function is a rule that pairs one output value to each input value. For eample, the rule might be multipl a number b and then subtract 1 from the result. The equation that represents this function is 1, where is the input and is the output. You can use a table to organize input and output values and write ordered pairs which can be graphed. Input Rule Output Ordered Pair 1 (, ) 1 ( 1) 1 3 ( 1, 3) 0 (0) 1 1 (0, 1) Amount of Ink 6 6 O Holt Mathematics

4 The function is a linear function because its graph is a nonvertical line. A linear function describes an output that is changing at a constant rate. Your child will learn to use functions to solve problems involving constant rates of change, such as rising temperatures. Your child will also look for patterns in sequences. In an arithmetic sequence, the same number is added to each term to get the net term. Eample:, 7, 10, 13, 3 is added to each term. In a geometric sequence, each term is multiplied b the same number to get the net term. Eample:, 8, 3, 18, Each term is multiplied b. The terms of a sequence can be written as outputs () in a function table. Input values are represented b n, the number of each term. This table helps to write a function that describes the arithmetic sequence above. n Rule 1 3(1) 1 3() (3) () 1 13 The rule is to multipl n b 3 and add 1. The function is 3n 1. To find the 6th term in the sequence, substitute 6 for n in the function. 3n 1 3(6) 1 19 The 6th term is 19. For additional resources, visit go.hrw.com and enter the keword MS7 Parent. Holt Mathematics

5 CHAPTER Famil Letter Section A What We Are Learning Dear Famil, Tables and Graphs Vocabular These are the math words we are learning: coordinate plane plane formed b horizontal and vertical number lines intersecting at zero on each ordered pair a pair of numbers that names a location on the coordinate plane origin the point where the aes intersect on a coordinate plane, has the coordinates (0, 0) quadrant one-quarter of the coordinate plane, bounded on two sides b the aes -ais horizontal number line in the coordinate plane -ais vertical number line in the coordinate plane Your child will be introduced to the coordinate plane, which is an etension of the number line. The coordinate plane is labeled below. II III F T O S Q The coordinate plane is divided into four quadrants b the - and -aes. The origin is the point where the aes intersect, identified b the ordered pair (0, 0). An ordered pair (, ) tells ou the - and -coordinates of a point. The -coordinate tells ou how far to move left or right from the origin. The -coordinate tells ou how far to move up or down. Your child will use these coordinates to plot points in all four quadrants. Draw a few points on the coordinate grid above and quiz our child to see if he or she can tell ou the ordered pairs that identif the points. I IV 9 Holt Mathematics

6 CHAPTER Famil Letter Section A, continued Your child will also learn about tables and graphs. A table is a useful wa to displa data. The table below shows how much mone was earned for each quantit of hours worked. Hours Worked Mone Earned $10 3 $1 $ 7 $3 B studing the numbers in the table, we learn that each amount of mone divided b the number hours is. This means that the job pas $ per hour. Another wa to see this relationship can be shown is b graphing this data. Mone Earned $3 $30 $ $0 $1 $10 $ You can see that both numbers increase with each entr. We can see this relationship in the height of the bars; each bar is higher than the last. We can also graph the data on the coordinate plane, using the figures in one column as the -coordinates and the figures in the other column as the -coordinates. Notice the similarities between the bar graph and the line graph. Look for sets of data in places such as newspapers and ask our child to think about what the graphs for these sets would look like. Would the bars increase or decrease in height? Seeing this information used in everda situations will help our child understand how the math relates to her or his life. Sincerel, 3 7 Hours Worked Holt Mathematics

7 Name Date Class CHAPTER Famil Letter Number Theor Identif the quadrant of each point in the diagram. 1. K. L 3. M. N Give the coordinates of each point.. A 6. B 7. C 8. D M K A D L O B N C Make a table for the graph below. Make a graph for the table below Food Served in the Cafeteria in a Month 1 1 Food Times Served 10 Macaroni and Cheese 3 8 Chicken Fingers 7 6 Hamburgers 6 Pizza 0 Mon Tues WedThurs Fri Hot Dogs Students Attendance Number of students Graph the data on a coordinate plane. 11. Miles Driven on a Road Trip Das Miles Answers: 1. Quadrant II. Quadrant I 3. Quadrant III. Quadrant IV. (, 3) 6. (, 3) 7. ( 1, ) 8. ( 3, ) 9. Da Students Das Mac & Chesse Chicken Hamburger Pizza Hot Dog Miles Times Served Monda Tuesda Wednesda Thursda Frida Holt Mathematics

8 Name Date Class CHAPTER Famil Fun Plotting Points Directions Solve each problem. Match the answer to an ordered pair and plot the point. Connect the ten points with straight lines to find the mster shape. (Hint: If ou plot all of the ordered pairs, ou will not get the correct answer.) ( ) 8 ( 8) ( 8) 7 ( 9) 3 ( 6) ( 10) 1 ( 38) 8 6 Ordered Pairs ( 8, ) Answer (0, 0) 0 (, ) ( 3, 0) ( 6, 3) ( 3, 3) 6 (3, 0) 1 (3, 3) O 6 8 (6, 3) 0 (3, 3) 8 ( 3, 3) 6 (, 1) (0, 6) Answers: 0,, 6, 6, 8, 1,, 30, 0, 8, The mster shape is a star. 3 Holt Mathematics

9 CHAPTER Famil Letter Section B What We Are Learning Functions Vocabular These are the math words we are learning: arithmetic sequence a sequence whose terms differ b the same number function a relationship that has one output for ever number ou input geometric sequence a sequence whose terms are multiplied b the same number to get the net term linear equation an equation whose graph is a straight line linear function a function whose graph is a non-vertical line sequence an ordered list of numbers Dear Famil, In this section our child will be introduced to the concept of functions. Your child will learn how to use tables to organize input and output values for a given function. He or she will then learn how to graph the ordered pairs on a coordinate sstem. Find the output for each input value. 1 for inputs 3, 6, 9 Input Rule Output 1 3 (3) (6) (9) 1 Substitute 3 for and simplif. Substitute 6 for and simplif. Substitute 9 for and simplif. The outputs are 1, 9, and. Your child will also be learning how to use tables and graphs as tools to identif patterns in a sequence. When a list of numbers follows a pattern, the numbers in the sequence are considered to be the output values of the function. Find a function that describes the sequence. Use the function to find the net three terms in the sequence. 6, 1, 18, n Rule Function: 6n Rule: multipl n b 6. The net three terms are 6 30, , and Holt Mathematics

10 CHAPTER Famil Letter Section B, continued The values calculated in a function table will help our child transition to graphing linear functions. Here is an eample of how our child will graph a linear function. Graph the linear function. 3 First, create an input/output table. Input Rule Output Ordered pairs 3 (, ) ( ) 3 7 (, 7) 0 (0) 3 3 (0, 3) () 3 1 (, 1) Because the equation is linear, plot three points on the coordinate plane and draw a straight line O 8 8 Help our child practice these skills. Create functions and ask our child to graph the function. This will strengthen a vital skill in our child s math education. Sincerel, 3 Holt Mathematics

11 Name Date Class CHAPTER Famil Letter Functions Find the output of each input value Input Rule Output 7 1 7( ) 1 7( ) 1 8 7( ) 1 Input Rule Output 3 1 3( ) 3( ) 3 3( ) Find the function that describes each sequence. Use the function to find the net three terms in the sequence. 3. 1, 1, 18, 1.,, 6, 8, 10. 0,, 8, 1, 16 Graph each function Answers: 1. 9, 13,.,, n 9;, 7, 30. n; 1, 1, 16. n ; 0,, 8, Holt Mathematics

12 Name Date Class CHAPTER Directions Famil Fun Magic Pictures Create our own magic b plotting the points to see what shape is revealed. Input Output Ordered pairs (, ) 6 1 (6, 1) 10 (, 10) 0 6 (0, 6) (, ) 6 0 (6, 0) 10 (10, ) 1 6 (1, 6) (10, 10) Answer: The mster shape is an octagon. 36 Holt Mathematics