Additional Practice
Additional Practice ACTIVITY 2.1
3.
In each of Items 1 through 4, one example is a function and the other is not. Identity each example as a function or not a function and explain why. 1.
UNIT 2
4
3 1
-2
-7
y 5 4 3
3
2
1
1 -5 -4 -3 -2 -1
-1
4
1
2
3
4
5
x
-2
-7
-2 -3
4. y = -2x + 3
-4
Given f (x) = 6 - 4x, g(x) = 2x2 + 3x - 4, and h(x) = 5x + 10, evaluate the following.
-5
5. h(4)
y
6. f (-2)
5
7. g(3)
4 3 2 1
© 2010 College Board. All rights reserved.
-5 -4 -3 -2 -1
-1
x = y2
1
2
3
4
-2 -3 -4 -5
2. {(-3, 6), (6, -3), (-6, 3), (3, -6)} {(4, 3), (1, 6), (6, 1), (4, 1)}
5
x
8. f (0.4) 1 9. g __ 2 2 10. h -__ 5
() ( )
ACTIVITY 2.2 11. Give the domain and range for the function 2 x. State whether this function f (x) = 3 - __ 3 is linear or not and explain how you determined this.
Algebra 1, Unit 2 • Linear Functions
1
Additional Practice
12. y = |x + 3| is graphed below. Give the domain and range. Is this relation a function? How do you know?
14. Give the domain and range for the relation graphed below. Explain whether or not this graph represents a function.
y
y
10
10
8
8
6
6
4
4
2 -10 -8 -6 -4 -2
-2
2 2
4
6
8 10
x
-2
-4
-4
-6
-6
-8
-8
-10
-10
13. y = x 2 - 3x + 4 is graphed below. Give the domain and range. Use the vertical line test to determine if y = x 2 - 3x + 4 is a function and explain how the vertical line test led you to your conclusion. y 10 8 6 4 2 -10 -8 -6 -4 -2
-2
2
4
6
8 10
x
-4 -6 -8 -10
2
-10 -8 -6 -4 -2
SpringBoard® Mathematics with Meaning™ Algebra 1
2
4
6
8 10
x
15. Samantha and Emerson are recording the distance traveled each second by a toy car rolling down a ramp. This table shows the data they have collected. Time (seconds)
2
Distance (centimeters)
8
3
4
5
6
7
8
9
12 16 20 24
The car stops after it has been rolling for 10 seconds. What is the range of the data the girls collected? Is the relation a function? Explain why or why not. ACTIVITY 2.3 16. Find ∆x and ∆y for the points (4, -5) and (-3, 2). 17. Lauren claims that the slope of the line through (-1, 8) and (4, 3) is the same as the slope of the line through (-6, 2) and (-8, 4). Prove or disprove the claim and explain your reasoning.
© 2010 College Board. All rights reserved.
UNIT 2
Additional Practice 18. An aircraft ascends to its cruising altitude at an average rate of 2400 feet per minute. It takes 15 minutes from the time it takes off to reach its cruising altitude. What is the cruising altitude? Explain how you reached your conclusion. 19. Does the table below represent data with a constant rate of change? Justify your answer. x
y
1 2 3 4
5 8 11 14
20. Calculate the slopes of the lines passing through (8, 9) and (-4, 18) and through (2, 4) and (0, 6). Use the slopes to compare and discuss the relative steepness of the two lines. 21. Find the slope of the line graphed below.
8 6 4 © 2010 College Board. All rights reserved.
Karsie has already saved $50 toward the purchase of a new MP3 player. She plans to save $15 more toward the purchase each week for the next several weeks. 25. Write a linear function that models this situation. 26. Karsie has decided she will not pay more than $200 for her new MP3 player. What is the maximum number of weeks she will need to save? The formula to convert degrees Fahrenheit, 5 F, to degrees Celsius, C, is C = __(F - 32). 9 27. Use the formula to convert 65°F to degrees Celsius. 28. Interpret the slope as a rate of change. 29. If the temperature is 120°Celsius, what is the temperature in degrees Fahrenheit?
30. Given that y varies directly as x and y = 50 when x = 5, what is the value of y when x = 3?
10
2 -2
ACTIVITY 2.4
ACTIVITY 2.5
y
-10 -8 -6 -4 -2
UNIT 2
2
4
6
8 10
x
-4 -6 -8 -10
The cost, C, of renting a canoe for h hours at a local park is given by the linear function C(h) = 10h + 20.
31. Which equation does not represent a direct variation? a. y = x x b. y = __ 4 2x c. y = __ 3 d. y = 3x - 7 32. Given that y varies inversely as x and y = 30 when x = 60, what is the value of y when x = 20?
22. What is the slope of this function? 23. Interpret the meaning of the slope in this situation. 24. How much does it cost to rent a canoe for 4 hours? Algebra 1, Unit 2 • Linear Functions
3
Additional Practice
The pay for an afterschool babysitting job varies directly with the number of hours worked. Brynn is paid $30.00 for 4 hours of babysitting. 33. Write an equation that relates the pay for the babysitting job to the number of hours worked.
ACTIVITY 2.7 41. Whitley and Holton are doing their math homework. The graphs give information on how much time it takes for them to complete their individual assignments. y
34. How much will Brynn be paid if she works 7 hours?
24 22
ACTIVITY 2.6 36. Write an equation of the line that has a slope 3 and a y-intercept of -8. of -__ 4 37. Write an equation of the line that passes through the point (-5, 4) and has a slope of -3.
Problems Assigned
20
35. How long will Brynn have to work to earn $200?
18 16 14 12 10 8 6 4 2
38. Find the slope and the y-intercept of the line with equation 3x - y - 7 = 0.
10 8 6
2
4
6
8 10
x
-4 -6 -8 -10
4
4
6 8 10 12 14 16 18 20 22 24 Minutes Holton works
22 20 18 16 14 12 10 8 6 2
2 -2
2
x
4
4
-10 -8 -6 -4 -2
6 8 10 12 14 16 18 20 22 24 Minutes Whitley works
24
Problems Assigned
y
4
y
39. Write an equation of the line passing through the points (-4, 6) and (-3, 8). 40. Given the graph below, write the equation of the line in slope-intercept form and in standard form.
2
SpringBoard® Mathematics with Meaning™ Algebra 1
x
a. If the students were assigned 36 problems, which student would spend more time on the assignment? What graphical evidence supports your conclusion?
© 2010 College Board. All rights reserved.
UNIT 2
Additional Practice b. Write the intercept form of the line for Whitley’s graph where y represents the problems assigned and x represents the number of minutes Whitley works. 42. Lines a and b cross the x- and y-axes at integer values. Write the intercept form of each line.
ACTIVITY 2.8 Jeremy collected data and created the scatter plot below to show the relationship between the day of the month and the amount of snow on the ground over a 24-day period in February. y
y
10 9
10
8
b
6 4 2
-10 -8 -6 -4 -2
-2
2
4
6
8 10
x
-4 -6 -8 -10
© 2010 College Board. All rights reserved.
43. The intercepts of a line have coordinates (-5, 0) and (0, 3). Write the intercept form of the line and graph it. 44. Given the standard form of the line 2x - 6y = 12, write the intercept form and give the x- and y-intercepts. 45. Verify that (1, 4) lies on the graph of the y x + __ line __ = 1. 5 5 46. If f (x) = 7x - 4, what is the zero of this function? How do you find it?
Inches of Snow
8 a
UNIT 2
7 6 5 4 3 2 1 2
4
6
8 10 12 14 16 18 20 22 24 Day in February
x
47. Why would (1, 9) and (22, 3.25) be reasonable points to select for writing a trend line for the data? 48. Use the points (1, 9) and (22, 3.25) to write a linear equation to model the data. 49. If the trend continues, how much snow will be on the ground on February 28? 50. Write the equation of the line containing the points (2, -4) and (-6, 8).
Algebra 1, Unit 2 • Linear Functions
5
3.
In each of Items 1 through 4, one example is a function and the other is not. Identity each example as a function or not a function and explain why. 1.
UNIT 2
4
3 1
-2
-7
y 5 4 3
3
2
1
1 -5 -4 -3 -2 -1
-1
4
1
2
3
4
5
x
-2
-7
-2 -3
4. y = -2x + 3
-4
Given f (x) = 6 - 4x, g(x) = 2x2 + 3x - 4, and h(x) = 5x + 10, evaluate the following.
-5
5. h(4)
y
6. f (-2)
5
7. g(3)
4 3 2 1
© 2010 College Board. All rights reserved.
-5 -4 -3 -2 -1
-1
x = y2
1
2
3
4
-2 -3 -4 -5
2. {(-3, 6), (6, -3), (-6, 3), (3, -6)} {(4, 3), (1, 6), (6, 1), (4, 1)}
5
x
8. f (0.4) 1 9. g __ 2 2 10. h -__ 5
() ( )
ACTIVITY 2.2 11. Give the domain and range for the function 2 x. State whether this function f (x) = 3 - __ 3 is linear or not and explain how you determined this.
Algebra 1, Unit 2 • Linear Functions
1
Additional Practice
12. y = |x + 3| is graphed below. Give the domain and range. Is this relation a function? How do you know?
14. Give the domain and range for the relation graphed below. Explain whether or not this graph represents a function.
y
y
10
10
8
8
6
6
4
4
2 -10 -8 -6 -4 -2
-2
2 2
4
6
8 10
x
-2
-4
-4
-6
-6
-8
-8
-10
-10
13. y = x 2 - 3x + 4 is graphed below. Give the domain and range. Use the vertical line test to determine if y = x 2 - 3x + 4 is a function and explain how the vertical line test led you to your conclusion. y 10 8 6 4 2 -10 -8 -6 -4 -2
-2
2
4
6
8 10
x
-4 -6 -8 -10
2
-10 -8 -6 -4 -2
SpringBoard® Mathematics with Meaning™ Algebra 1
2
4
6
8 10
x
15. Samantha and Emerson are recording the distance traveled each second by a toy car rolling down a ramp. This table shows the data they have collected. Time (seconds)
2
Distance (centimeters)
8
3
4
5
6
7
8
9
12 16 20 24
The car stops after it has been rolling for 10 seconds. What is the range of the data the girls collected? Is the relation a function? Explain why or why not. ACTIVITY 2.3 16. Find ∆x and ∆y for the points (4, -5) and (-3, 2). 17. Lauren claims that the slope of the line through (-1, 8) and (4, 3) is the same as the slope of the line through (-6, 2) and (-8, 4). Prove or disprove the claim and explain your reasoning.
© 2010 College Board. All rights reserved.
UNIT 2
Additional Practice 18. An aircraft ascends to its cruising altitude at an average rate of 2400 feet per minute. It takes 15 minutes from the time it takes off to reach its cruising altitude. What is the cruising altitude? Explain how you reached your conclusion. 19. Does the table below represent data with a constant rate of change? Justify your answer. x
y
1 2 3 4
5 8 11 14
20. Calculate the slopes of the lines passing through (8, 9) and (-4, 18) and through (2, 4) and (0, 6). Use the slopes to compare and discuss the relative steepness of the two lines. 21. Find the slope of the line graphed below.
8 6 4 © 2010 College Board. All rights reserved.
Karsie has already saved $50 toward the purchase of a new MP3 player. She plans to save $15 more toward the purchase each week for the next several weeks. 25. Write a linear function that models this situation. 26. Karsie has decided she will not pay more than $200 for her new MP3 player. What is the maximum number of weeks she will need to save? The formula to convert degrees Fahrenheit, 5 F, to degrees Celsius, C, is C = __(F - 32). 9 27. Use the formula to convert 65°F to degrees Celsius. 28. Interpret the slope as a rate of change. 29. If the temperature is 120°Celsius, what is the temperature in degrees Fahrenheit?
30. Given that y varies directly as x and y = 50 when x = 5, what is the value of y when x = 3?
10
2 -2
ACTIVITY 2.4
ACTIVITY 2.5
y
-10 -8 -6 -4 -2
UNIT 2
2
4
6
8 10
x
-4 -6 -8 -10
The cost, C, of renting a canoe for h hours at a local park is given by the linear function C(h) = 10h + 20.
31. Which equation does not represent a direct variation? a. y = x x b. y = __ 4 2x c. y = __ 3 d. y = 3x - 7 32. Given that y varies inversely as x and y = 30 when x = 60, what is the value of y when x = 20?
22. What is the slope of this function? 23. Interpret the meaning of the slope in this situation. 24. How much does it cost to rent a canoe for 4 hours? Algebra 1, Unit 2 • Linear Functions
3
Additional Practice
The pay for an afterschool babysitting job varies directly with the number of hours worked. Brynn is paid $30.00 for 4 hours of babysitting. 33. Write an equation that relates the pay for the babysitting job to the number of hours worked.
ACTIVITY 2.7 41. Whitley and Holton are doing their math homework. The graphs give information on how much time it takes for them to complete their individual assignments. y
34. How much will Brynn be paid if she works 7 hours?
24 22
ACTIVITY 2.6 36. Write an equation of the line that has a slope 3 and a y-intercept of -8. of -__ 4 37. Write an equation of the line that passes through the point (-5, 4) and has a slope of -3.
Problems Assigned
20
35. How long will Brynn have to work to earn $200?
18 16 14 12 10 8 6 4 2
38. Find the slope and the y-intercept of the line with equation 3x - y - 7 = 0.
10 8 6
2
4
6
8 10
x
-4 -6 -8 -10
4
4
6 8 10 12 14 16 18 20 22 24 Minutes Holton works
22 20 18 16 14 12 10 8 6 2
2 -2
2
x
4
4
-10 -8 -6 -4 -2
6 8 10 12 14 16 18 20 22 24 Minutes Whitley works
24
Problems Assigned
y
4
y
39. Write an equation of the line passing through the points (-4, 6) and (-3, 8). 40. Given the graph below, write the equation of the line in slope-intercept form and in standard form.
2
SpringBoard® Mathematics with Meaning™ Algebra 1
x
a. If the students were assigned 36 problems, which student would spend more time on the assignment? What graphical evidence supports your conclusion?
© 2010 College Board. All rights reserved.
UNIT 2
Additional Practice b. Write the intercept form of the line for Whitley’s graph where y represents the problems assigned and x represents the number of minutes Whitley works. 42. Lines a and b cross the x- and y-axes at integer values. Write the intercept form of each line.
ACTIVITY 2.8 Jeremy collected data and created the scatter plot below to show the relationship between the day of the month and the amount of snow on the ground over a 24-day period in February. y
y
10 9
10
8
b
6 4 2
-10 -8 -6 -4 -2
-2
2
4
6
8 10
x
-4 -6 -8 -10
© 2010 College Board. All rights reserved.
43. The intercepts of a line have coordinates (-5, 0) and (0, 3). Write the intercept form of the line and graph it. 44. Given the standard form of the line 2x - 6y = 12, write the intercept form and give the x- and y-intercepts. 45. Verify that (1, 4) lies on the graph of the y x + __ line __ = 1. 5 5 46. If f (x) = 7x - 4, what is the zero of this function? How do you find it?
Inches of Snow
8 a
UNIT 2
7 6 5 4 3 2 1 2
4
6
8 10 12 14 16 18 20 22 24 Day in February
x
47. Why would (1, 9) and (22, 3.25) be reasonable points to select for writing a trend line for the data? 48. Use the points (1, 9) and (22, 3.25) to write a linear equation to model the data. 49. If the trend continues, how much snow will be on the ground on February 28? 50. Write the equation of the line containing the points (2, -4) and (-6, 8).
Algebra 1, Unit 2 • Linear Functions
5
