Skills Practice Skills Practice for Lesson 1.1

Transcription

1 Skills Practice Skills Practice for Lesson. Name Date Tanks a Lot Introduction to Linear Functions Vocabulary Define each term in your own words.. function 2. linear function 3. independent variable 4. dependent variable 200 Carnegie Learning, Inc. 5. variable Problem Set Determine the independent quantity and the dependent quantity in each example.. A car is traveling at a rate of sixty miles per hour for several hours. independent quantity: time in hours dependent quantity: distance in miles Chapter l Skills Practice 297

2 2. Sharon is growing at a rate of two inches per year. 3. The area of a square floor is the product of the length of two of its sides. 4. The perimeter of a square is the sum of the length of all four of its sides. 5. The length of a video file in minutes relates to the size of the file in bytes. 6. The total weight of a bag of apples in pounds relates to the number of apples in the bag. Define a variable to represent each of the quantities. Then write an equation that shows the relationship between the two variables. 7. A runner travels 4 miles per hour. Write an equation to show the relationship between the total distance the runner travels and the time. Let t represent the amount of time in hours. Let d represent the distance the runner travels in miles. d 4t 200 Carnegie Learning, Inc. 8. Each DVD at an electronics store costs $2.50. Write an equation to show the relationship between the total cost when purchasing DVDs and the number of DVDs. 298 Chapter l Skills Practice

3 Name Date 9. To make one solar panel, a company uses two kilograms of silicon. The company has 00 kilograms of silicon. Write an equation to show the relationship between the amount of silicon remaining and the number of solar panels made. 0. A bowling ball company uses seven pounds of resin to make one seven-pound bowling ball. They have a total of 490 pounds of resin. Write an equation to show the relationship between the amount of resin remaining and the number of seven-pound bowling balls made.. Julia opens a bank account and deposits $500 into the account. Each month, she deposits $50 into the account. Write an equation to show the relationship between the total amount of money in her bank account and the number of months since she opened the account. 200 Carnegie Learning, Inc. 2. A water tower contains 5,000 gallons of water. Each week, 2500 gallons of water are used and 000 gallons of water are added. Write an equation to show the relationship between the total amount of water remaining in the water tower and the number of weeks that have elapsed. Chapter l Skills Practice 299

4 Graph each linear function. 3. y 2 x 4. y 3x 2 y 4 3 y = 2x x y x 2 6. y 2 x y 4x y 2x Carnegie Learning, Inc. 300 Chapter l Skills Practice

5 Name Date Use the given information to answer each question. 9. The distance, d, in miles that a plane travels can be modeled by the equation d 550t, where t represents the time in hours. If the plane travels for 7 hours, how far will it go? d 550t d 550(7) d 3850 The plane will travel 3850 miles in 7 hours. 20. The distance, d, in feet that a fly travels can be modeled by the equation d 5t, where t represents the time in seconds. If the fly travels for 30 seconds, how far will it have gone? 200 Carnegie Learning, Inc. 2. The equation w,000,000 20m shows the amount of water, w, in gallons remaining in a water tower, where m represents the number of minutes that have passed. When will there be 750,000 gallons of water in the water tower? Chapter l Skills Practice 30

6 22. The equation a t shows the amount of money, a, in dollars remaining in a bank account where t represents the time in weeks. When will the balance in the account be $000? 23. A ticket seller s weekly earning, s, in dollars can be modeled by the equation s 0.0t 350, where t represents the number of tickets he sells. How many tickets will the ticket seller have to sell to make $440 that week? 24. The total number of computers, c, that a company can manufacture can be modeled by the equation c s 250, where s represents the number of 50 screws that they need to order. How many screws will they need to order so that they can manufacture 525 computers? 200 Carnegie Learning, Inc. 302 Chapter l Skills Practice

7 Skills Practice Skills Practice for Lesson.2 Name Date Calculating Answers Solving Linear Equations and Linear Inequalities in One Variable Vocabulary Write the term that best completes each statement.. The solution of an inequality can be graphed on a(n). 2. Adding, subtracting, multiplying, and distributing are all examples of that can be used to solve an equation. 3. Addition, subtraction, multiplication, and division are the four basic that can be applied to both sides of a linear equation to solve the equation. 4. A(n) is a statement that compares two expressions. Problem Set Indicate which transformation(s) are needed to solve each equation.. x 4 2. x 3 2 Add to both sides. 200 Carnegie Learning, Inc. 3. 2x x x 4 7 x Chapter l Skills Practice 303

8 S olve each equation. 7. x x x x x x x 3 2. x x 3 4. x Carnegie Learning, Inc. 304 Chapter l Skills Practice

9 Name Date 5. 2 x 5 5 3x 6. 4x 3x 9 2 x S olve each inequality. Graph the solution on a number line. 7. 3x x 5 7 3x x 6 3x x x x 200 Carnegie Learning, Inc. 2. 2x x 4 3 Chapter l Skills Practice 305

10 23. 2( x 3) (2x 5) 25. x x Carnegie Learning, Inc. 306 Chapter l Skills Practice

11 Skills Practice Skills Practice for Lesson.3 Name Date Running a 0K Slope-Intercept Form of Linear Functions Vocabulary Determine each of the following for the linear function 2 x 3y 6.. slope 2. y-intercept 3. slope-intercept form 4. x-intercept Problem Set Identify the slope of each linear function.. y 2 x 3 2. y 3x 4 The slope is Carnegie Learning, Inc. 3. y 2 x 3 2 Identify the y-intercept of each linear function. 4. y 5 x y 5x 2 6. y x 3 The y-intercept is y 2 x y 3 3 x 2 2 Chapter l Skills Practice 307

12 Write a linear equation in slope-intercept form for each situation. 9. Louise opens a bank account and deposits $250. Every month she deposits $50 into her account. Write an equation to represent the amount she has in her account after x months. y 50x Erin opens a bank account and deposits $350. Every month she withdraws $25 from her account. Write an equation to represent the amount she has in her account after x months.. A computer is downloading a 00-megabyte program file. It downloads the program at a rate of 5 megabytes per minute. Write an equation to represent the number of megabytes left to download after x minutes. 2. Marco has 20 gigabytes of computer programs on his computer. Every month he adds.5 gigabytes of programs to his computer. Write an equation to represent the number of gigabytes of programs he has on his computer after x months. Calculate the slope and y-intercept for each function. 3. A linear function passes through the points (0, 0) and (4, 8). The y-intercept is 0. m y 2 y 8 0 x 2 x 4 0 The slope is A linear function passes through the points (0, 0) and (3, 27). 200 Carnegie Learning, Inc. 308 Chapter l Skills Practice

13 Name Date 5. A linear function passes through the points ( 4, 9) and (3, 5). 6. A linear function passes through the points ( 5, 2) and (3, 0). 200 Carnegie Learning, Inc. 7. A linear function passes through the points (3, 0) and (4, 2). Chapter l Skills Practice 309

14 8. A linear function passes through the points ( 2, 6) and ( 4, 0). Graph each linear function using its slope and y-intercept. 9. y x y 2x 3 Slope y-intercept 2 y y = x x Carnegie Learning, Inc. 30 Chapter l Skills Practice

15 Name Date 2. y 3 x 22. y 2 2 x 23. y y Carnegie Learning, Inc. Chapter l Skills Practice 3

16 200 Carnegie Learning, Inc. 32 Chapter l Skills Practice

17 Skills Practice Skills Practice for Lesson.4 Name Date Pump It Up Standard Form of Linear Functions Vocabulary Give an example of each key term.. standard form of a linear equation 2. slope-intercept form of a linear equation Problem Set For each linear equation written in standard form, calculate the x- and y-intercepts. Use the intercepts to graph the equation.. x y 3 2. x y 2 x y 3 x 3 y 3 x-intercept 3; y-intercept Carnegie Learning, Inc. y 4 3 (0, 3) 2 (3, 0) x Chapter l Skills Practice 33

18 3. 2x 3y 6 4. x 2y x 5y x 4y Carnegie Learning, Inc. 34 Chapter l Skills Practice

19 Name Date 7. 2 x y 3 8. x 3y 5 Rewrite each linear equation in slope-intercept form. 9. x y 2 0. x y y x Carnegie Learning, Inc.. 2x y x y x 3y x 3y x 2y 6. x 5y 0 Chapter l Skills Practice 35

20 Rewrite each linear equation in standard form. 7. y 2 x 3 8. y 4x 5 2 x y 3 9. y x y x 2. y 5 x y 4 5 x Carnegie Learning, Inc. 36 Chapter l Skills Practice

21 Skills Practice Skills Practice for Lesson.5 Name Date Shifts and Flips Basic Functions and Linear Transformations Vocabulary Write the term that best completes each statement.. A function undergoes a(n) when it is stretched or shrunk. 2. A(n) is a line in which a function is flipped so that it mirrors itself. 3. A(n) is a transformation in which a function is flipped over a given line. 4. The function y x is the of the function y 2 x 3. Problem Set Indicate the algebraic transformation which was performed on the basic function to result in each transformed function.. y x 2 2. y x Add y 4x 4. y 5 x 200 Carnegie Learning, Inc. Indicate the graphical transformation(s) which were performed on the basic function to result in each transformed function. 5. y x 3 Move the graph down 3 units. 6. y x 7. y 2 x 3 8. y 3x 4 Chapter l Skills Practice 37

22 9. y 2 x 3 0. y 5 3 x 4 Graph each set of equations on the same grid. Compare the graphs of the lines. Then determine whether the graphs of the lines are parallel, perpendicular, or neither.. y x 3 and y x 2. y 2 x and y 4x y 4 3 y = x + 2 y = x x The first graph is shifted two units up from the second graph. The lines are parallel. 200 Carnegie Learning, Inc. 38 Chapter l Skills Practice

23 Name Date 3. y x and y x 2 4. y x 2 and y 2x y 2 3 x 2 and y 2 3 x 2 6. y x 3 and y 4 2 x 200 Carnegie Learning, Inc. Chapter l Skills Practice 39

24 7. y x and y 5x 8. y x 2 and y x y 2 x and y 2 x y 0 and y Carnegie Learning, Inc. 320 Chapter l Skills Practice

25 Skills Practice Skills Practice for Lesson.6 Name Date Inventory and Sand Determining the Equations of Linear Functions Vocabulary Identify the similarities and differences between each pair of key terms.. point-slope form and two-point form 2. parallel lines and perpendicular lines Problem Set Determine the slope-intercept form of the equation of each line.. Slope 2 and y-intercept 3 2. Slope 4 and y-intercept Carnegie Learning, Inc. y 2 x 3 3. Slope and y-intercept 4 4. Slope and y-intercept 2 Determine the slope-intercept form of the equation of each line. 5. Slope 5 and the line passes 6. Slope 0 and the line passes through the point (2, 3) through the point (3, 5) y 3 5( x 2) y 3 5x 0 y 5x 3 Chapter l Skills Practice 32

26 7. Slope 7 and the line passes through 8. Slope 3 and the line passes the point (, 4) through the point (5, 6) Determine the slope-intercept form of the equation of the line passing through each pair of points. 9. (, 2) and (5, 3) 0. (2, 6) and (5, 8) m y 3 ( x 5) 4 y 5 x y x ( 2, 5) and (4, 3) 2. (, 7) and (5, 3) 3. (0, 3) and (, 3) 4. (2, 4) and (3, 4) 200 Carnegie Learning, Inc. 322 Chapter l Skills Practice

27 Name Date Determine the slope-intercept form of the equation of each line, given the equation of a line parallel to the line and a point on the line. 5. y 3x 2, (, 4) 6. y 5x 6, (3, 5) 4 3() b b y 3x 7. y 2 x 3, ( 2, 6) 8. y 4x, (3, 4) 9. y x, (6, 5) 20. y 3 x 0, (4, 3) Carnegie Learning, Inc. Determine the slope-intercept form of the equation of each line, given the equation of a line perpendicular to the line and a point on the line. 2. y 3x, (2, 4) 22. y 4x 3, (, ) m m 2 3 y 4 ( x 2) 3 y x y 3 x 4 3 Chapter l Skills Practice 323

28 23. y x 2, (3, 2) 24. y 3 x 9, ( 5, ) y x 6, (0, 3) 26. y x 2, (, 0) Carnegie Learning, Inc. 324 Chapter l Skills Practice

29 Skills Practice Skills Practice for Lesson.7 Name Date Absolutely! Absolute Value in Equations and Inequalities in One and Two Variables Vocabulary Match each example with the term that describes it.. x 2 3 a. absolute value expression 2. 3x b. absolute value equation x 2 5 c. absolute value inequality x 5 8 d. compound inequality 200 Carnegie Learning, Inc. Problem Set Solve each equation.. x x 2 5 x 3 4 x 3 4 x 7, 3. x x Chapter l Skills Practice 325

30 5. 2x x 4 Graph each equation. 7. y x 3 8. y x 2 y y = x x y 3x 6 0. y 4x Carnegie Learning, Inc. 326 Chapter l Skills Practice

31 Name Date. y x 3 2. y 2x 8 Solve each inequality and graph its solution on a number line. 3. 3x x x 2 3 or 3x 2 3 3x 9 or 3x 5 x 3 or x x x Carnegie Learning, Inc x x 2 Chapter l Skills Practice 327

32 Graph each inequality. 9. y x y x y 4 y > x x y 3x y x y 4x y 3x Carnegie Learning, Inc. 328 Chapter l Skills Practice

33 Skills Practice Skills Practice for Lesson.8 Name Date Inverses and Pieces Functional Notation, Inverses, and Piecewise Functions Vocabulary Give an example of each term.. relation 2. domain 3. range 4. function 5. inverse operations 200 Carnegie Learning, Inc. 6. functional notation 7. identity function 8. inverse functions Chapter l Skills Practice 329

34 9. composition of functions 0. piecewise function Problem Set Rewrite each linear function using functional notation.. y 2x 3 2. y 3x f( x) 2 x x 3y x 2y 2 Calculate the value of each function for the given values of the independent variable. 5. f( x) 2x, calculate f( ) and f(2) f( ) 2; f(2) 4 6. f( x) x, calculate f( 3) and f(4) 7. k( x) 3x 5, calculate k( 5) and k(8) 8. k( x) 4x 2, calculate k(0) and k(6) 9. g( x) x 2 2x, calculate g( 3) and g(2) 200 Carnegie Learning, Inc. 0. g( x) 2x 2 3, calculate g( ) and g(4) 330 Chapter l Skills Practice

35 Name Date Determine the inverse of each function.. f( x) 4x 2. f( x) 2x f ( x) 4 x 3. g( x) 5x 2 4. g( x) 3x 4 5. h( x) 2.3x.3 6. h( x) 4.5x 5.6 For the functions f( x) x 2 and g( x) 3x, calculate each composition. 7. f(g(2)) 8. g(f(2)) f(g(2)) f( 6) g(f( 3)) 20. f(g( 3)) 2. f(f(2)) 22. g(g(2)) 200 Carnegie Learning, Inc. Graph each piecewise function. 23. f( x) 2x x 2 x 4 x 2 y f( x) x 4 x 2x x x 2 3 Chapter l Skills Practice 33

36 25. g( x) x x 2x x 2 x 2 x g( x) x x 4 2x 3 4 x x x Write a piecewise function to model each situation. 27. A rental car company charges $0.35 per mile for the first 200 miles. After 200 miles they charge $0.20 per mile. Let c(m) be the cost for driving m miles. c(m) 0.35m m m m A laundromat charges $.25 per pound of laundry for the first 0 pounds needed to be cleaned. After 0 pounds they charge $0.75 per pound. Let c(l) be the cost for cleaning l pounds of laundry. 29. A movie theatre charges $5.00 per ticket for people between the ages of 0 and 5 years. They charge $7.50 per ticket for people above the age of 5. Let c(a) be the cost of a movie if a person s age is a years. 200 Carnegie Learning, Inc. 30. A garage will inflate bicycle tires that are smaller than 20 inches in diameter for $.50. They charge $2.25 to inflate bicycle tires that are 20 inches or larger. Let c(d ) be the cost to inflate a bicycle tire that has a diameter of d inches. 332 Chapter l Skills Practice

37 Name Date 3. A home-and-garden store charges $0.25 for a cubic yard of gravel if you buy 0 cubic yards or less. They charge $9.50 for a cubic yard of gravel if you buy between 0 and 5 cubic yards. They charge $8.75 for a cubic yard of gravel if you buy 5 cubic yards or more. Let c( y) be the cost of y cubic yards of gravel. 32. An airline charges different ticket prices based on the number of miles a plane travels. If a plane travels less than 500 miles, an airline will charge $0.85 per mile. If a plane travels 500 miles to 500 miles, they charge $0.70 per mile. If a plane travels more than 500 miles, they charge $0.55 per mile. Let c(m) be the cost to fly m miles. 200 Carnegie Learning, Inc. Chapter l Skills Practice 333

38 200 Carnegie Learning, Inc. 334 Chapter l Skills Practice