TOPIC ESSENTIAL QUESTION
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1 TOPIC Topic Review TOPIC ESSENTIAL QUESTION 1. How can linear functions be used to model situations and solve problems? Vocabular Review Choose the correct term to complete each sentence.. When tends to increase as increases, the two data sets have a.. A(n) is the difference between an actual and a predicted data value.. A(n) is an ordered list of numbers that often forms a pattern.. A trend line that most closel models the relationship between two variables displaed in a scatter plot is the.. The measures the strength and direction of the relationship between two variables in a linear model. arithmetic sequence correlation coefficient line of best fit linear regression positive association residual sequence term of a sequence trend line Concepts & Skills Review LESSON -1 Relations and Functions A function is a relation in which ever input, or element of the domain, is associated with eactl one output, or element of the range. Identif the domain and range of the ordered pairs in the table. Do the ordered pairs represent a function? Justif our response The domain is {,,,, }. The range is {., 1., 1.,., 7.}. Each element of the domain is associated with eactl one element of the range, so the ordered pairs represent a function. Identif the domain and range of each relation. Is the relation a function? Eplain. 7. {(, 1), (, ), (, ), (, )}. 1 Reason For and 1, would a reasonable domain include all real numbers? Eplain.. A person drinks n ounces of a -ounce bottle of a sports drink. 1. A printer prints p pages at a rate of pages per minute. Construct Arguments What constraints, if an, are there on the domain? Eplain. 11. An airplane ascends to a cruising altitude at the rate of 1, ft/min for m minutes. 1. The value of an automobile in d dollars decreases b about 1% each ear. TOPIC REVIEW TOPIC Topic Review 1
2 LESSON - Linear Functions A linear function is a function whose graph is a straight line. It represents a linear relationship between two variables. A linear function written in function notation is f() = m + b and f() is read f of. A tai compan charges $. plus $. per mile. What linear function can be used to determine the cost of a tai ride of miles? How much would a.-mile tai ride cost? Let d = distance of the tai ride. Cost of tai ride = cost distance + fee f(d) =.d +. Use the function to determine the cost of a.-mile ride. f(.) = (.)(.) +. =.7 The cost of a.-mile tai ride is $.. Practice and Problem Solving Evaluate each function for the elements in the domain {,,,, }. 1. f() = 1 1. f(t) = (t ) 1. Make Sense and Persevere Melissa runs a graphic design business. She charges b the page, and has a setup fee. The table shows her earnings for the last few projects. What is her per-page rate, and what is her setup fee? Cost ($) Page totals 1 1. Use Structure Tia s Computer Repair Shop charges the labor rates shown for computer repairs. What linear function can she use to determine the cost of a repair that takes. hours and includes $1 in parts? Hours Labor ($) LESSON - Transforming Linear Functions A transformation of a function f maps each point of its graph to a new location. A translation shifts each point of the graph of a function the same distance horizontall, verticall, or both. Stretches and compressions scale each point of a graph either horizontall or verticall. Let f() = 1. If g() = ( 1) +, how does the graph of g compare to the graph of f? g O f The graph of g is the translation of the graph of f three units up. Given the function f() =, how does the addition or subtraction of a constant to the output affect the graph? 17. f() = 1. f() = + Given f() =, describe how the graph of g compares with the graph of f. 1. g() = ( ). g() = ( ) 1. Reason Given f() = +, how does multipling the output of f b affect the slope and -intercept of the graph?. Model With Mathematics A hotel business center charges $ per hour to rent a computer plus a $ securit deposit. The total rental charge is represented b f() = +. How would the equation change if the business center increased the securit deposit b $1? 1 TOPIC Linear Functions Go Online PearsonRealize.com
3 LESSON - Arithmetic Sequences A sequence is an ordered list of numbers that often follows a pattern. Each number is a term of the sequence. In an arithmetic sequence, the difference between an two consecutive terms is a constant called the common difference, d. The recursive formula is used to describe the sequence and find the net term in a sequence from a given term. The eplicit formula is used to find a specific term of the sequence. What is the 1th term in the sequence shown?,.,,.,., Determine the recursive formula to describe the sequence. The common difference, d, is.. a 1 = a n = a n 1 +. Use the eplicit formula to find the 1th term. a 1 = + (1 1). a 1 = 1. The 1th term of the sequence is 1.. Tell whether each sequence is an arithmetic sequence. If it is, give the common difference. If it is not, eplain wh..,, 1,,,.,, 1, 7,, Write a recursive formula for each arithmetic sequence..,, 1, 1, 1,.,., 1, 1., 1, 7. Reason A table of data of an arithmetic sequence is shown. Use the eplicit formula for the arithmetic sequence to find the 1th term Make Sense and Persevere Gabriela is selling friendship bracelets for a school fundraiser. After the first da, she has bracelets left. After the second da, she has left. Assuming the sales pattern continues and it is an arithmetic sequence, how man bracelets will Gabriela have left to sell after the fifth da? TOPIC REVIEW TOPIC Topic Review 17
4 LESSON - Scatter Plots and Lines of Fit A paired data set (or a bivariate data set) has a positive association when -values tend to increase as -values increase and a negative association when -values tend to decrease as -values increase. When the relationship between the paired data can be modeled with a linear function, a line of best fit represents the relationship. The paired data are positivel correlated if -values increase as -values increase and negativel correlated if -values decrease as -values increase. Yama takes a course to improve his tping speed. The scatter plot shows his progress over si weeks. What is the relationship between the number of weeks and Yama's tping speed? Words Tped per Minute 1 Week Describe the tpe of association each scatter plot shows Reason Where should the line of best fit be in relationship to the points plotted on a scatter plot? Use Appropriate Tools For each table, make a scatter plot of the data. If the data suggest a linear relationship, draw a trend line and write its equation... As the number of weeks of practice increase, so does the number of words tped per minute. The scatter plot shows a positive association that is approimatel linear suggesting a positive correlation between weeks and words tped per minute Model With Mathematics The table shows the recommended distance of a light source in feet, from the wall for different ceiling heights in feet. What is the equation of the trend line that models the data shown in the table? What does the slope of the trend line represent? TOPIC Linear Functions Go Online PearsonRealize.com
5 LESSON - Analzing Lines of Fit Linear regression is a method used to calculate line of best fit. The correlation coefficient indicates the direction and strength of the linear relationship between two variables. A residual reveals how well a linear model fits the data set. You can use the line of best fit to estimate a value within a range of known values (interpolation) or predict a value outside the range of known values (etrapolation). The scatter plot shows the percentage of American adults with a high school diploma or higher from 1 to 1. Based on the residual plot below the scatter plot, how appropriate is the linear model for the data? Adult Population in U.S. With High School Diploma or Higher (Percent) Educational Attainment Years Since Residual Plot f() =.17 +.; r =.11 Use technolog to perform a linear regression to determine the equation for the line of best fit for the data. Estimate the value of when = Reason How are interpolation and etrapolation similar? How are the different?. Model With Mathematics The table shows the winning times for the 1-meter run in the Olmpics since 1. What is the equation of the line of best fit for the data? What do the slope and -intercept represent? Estimate the winning time in 1, and predict the winning time in. Year Time (s) Year Time (s) TOPIC REVIEW.. Years Since 1 The residual plot shows the residuals distributed above and below the -ais and clustered somewhat close to the -ais. The linear model is likel a good fit for the data. TOPIC Topic Review 1
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