3 answers
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1. Compare Linear Function 1 with Linear Function 2. Which one has the greater rate of change?
Linear Function 1: y=15x+8
Linear Function 2:
x y
5 26
13 34(1 point)
Responses
A. Linear Function 1 has the greater rate of change, with a rate of change equal to 8 while Linear Function 2 has a rate of change equal to 1.
B. Linear Function 1 has the greater rate of change, with a rate of change equal to 15 while Linear Function 2 has a rate of change equal to 1.
C. Linear Function 2 has the greater rate of change, with a rate of change equal to 21 while Linear Function 1 has a rate of change equal to 8.
D. Linear Function 2 has the greater rate of change, with a rate of change equal to 21 while Linear Function 1 has a rate of change equal to 15.
2. Compare Linear Function 1 with Linear Function 2. Which one has the lesser initial value?
Linear Function 1: Lionel’s cell phone plan costs $45 per month.
Linear Function 2: The relationship between the number of months Ruby has had her cell phone (x) and the total cost (y) is given by y=40x+60 .
(1 point)
Responses
A. Linear Function 1 has the lesser initial value, with an initial value equal to $0 while Linear Function 2 has an initial value equal to $60.
B. Linear Function 1 has the lesser initial value, with an initial value equal to $0 while Linear Function 2 has an initial value equal to $40.
C. Linear Function 1 has the lesser initial value, with an initial value equal to $45 while Linear Function 2 has an initial value equal to $60.
D. Linear Function 2 has the lesser initial value, with an initial value equal to $40 while Linear Function 1 has an initial value equal to $45.
3. A function has an initial value of −1 and a slope equal to 3. Choose the sketch of a graph that exhibits the qualitative features of the function.(1 point)
Responses
A. A coordinate plane with four quadrants shows the x and y axes ranging from negative 8 to 8 in increments of 1. An upward line with arrows on both the ends passes through the first, fourth, and third quadrants. The line intersects the x-axis at left parenthesis 0.3 comma 0 right parenthesis and the y-axis at left parenthesis 0 comma negative 1 right parenthesis. Values are approximate.
B. A coordinate plane with four quadrants shows the x and y axes ranging from negative 8 to 8 in increments of 1. An upward line with arrows on both the ends passes through the first, second, and third quadrants. The line intersects the x-axis at left parenthesis negative 1 comma 0 right parenthesis and the y-axis at left parenthesis 0 comma 3 right parenthesis.
C. A coordinate plane with four quadrants shows the x and y axes ranging from negative 8 to 8 in increments of 1. An upward line with arrows on both the ends passes through the first, fourth, and third quadrants. The line intersects the x-axis at left parenthesis 3 comma 0 right parenthesis and the y-axis at left parenthesis 0 comma negative 1 right parenthesis.
D. A coordinate plane with four quadrants shows the x and y axes ranging from negative 8 to 8 in increments of 1. A downward line with arrows on both the ends passes through the second, first, and fourth quadrants. The line intersects the x-axis at left parenthesis 3 comma 0 right parenthesis and the y-axis at left parenthesis 0 comma 3 right parenthesis.
4. Willow is rereading her favorite book. She starts the day on page 15. Looking at the clock, she realizes that she can read 2 pages every minute. Choose the sketch of a graph that shows the relationship between the number of minutes Willow has been reading today and the page number she is on.(1 point)
Responses
A. A coordinate plane shows the x-axis, labeled as Number of Minutes, ranging from negative 2 to 30 in increments of 2, and the y-axis, labeled as Page Number, ranging from negative 5 to 100 in increments of 5. A ray extends from a plotted point. The coordinates of a plotted closed circle are left parenthesis 2 comma 0 right parenthesis. An upward slanting arrow extends from the plotted point and passes through left parenthesis 8 comma 90 right parenthesis.
B. A coordinate plane shows the x-axis, labeled as Number of Minutes, ranging from negative 2 to 30 in increments of 2, and the y-axis, labeled as Page Number, ranging from negative 5 to 100 in increments of 5. A ray extends from a plotted point. The coordinates of the plotted closed circle are left parenthesis 0 comma 15 right parenthesis. An upward slanting arrow extends from the plotted point and passes through left parenthesis 30 comma 75 right parenthesis.
C. A coordinate plane shows the x-axis, labeled as Number of Minutes, ranging from negative 2 to 30 in increments of 2, and the y-axis, labeled as Page Number, ranging from negative 5 to 100 in increments of 5. A ray extends from a plotted point. The coordinates of a plotted closed circle are left parenthesis 0 comma 2 right parenthesis. An upward slanting arrow extends from the plotted point and passes through left parenthesis 6 comma 92 right parenthesis
D. A coordinate plane shows the x-axis, labeled as Number of Minutes, ranging from negative 2 to 30 in increments of 2, and the y-axis, labeled as Page Number, ranging from negative 5 to 100 in increments of 5. A ray extends from a plotted point. The coordinates of a plotted closed circle are left parenthesis 2 comma 0 right parenthesis. An upward slanting arrow extends from the plotted point and passes through left parenthesis 8 comma 90 right parenthesis.
5. Jasmine is running in a race. She runs 1,500 meters in 7 minutes. She starts out fast, slows down toward the middle of the race, and then finishes by sprinting to the finish line. Choose the sketch of a graph that exhibits the qualitative features of the relationship between the number of minutes Jasmine has been running and the distance she has run.(1 point)
Responses
A. A coordinate plane shows the x-axis, labeled as Number of Minutes, ranging from 0 to 10 in increments of 1, and the y-axis, labeled as Number of Meters, ranging from 0 to 1600 in increments of 100. A curve with a closed circle at both the ends is shown. The coordinates of a plotted closed circle are left parenthesis 0 comma 0 right parenthesis. An upward curve extends from this point and increases steeply to left parenthesis 4 comma 900 right parenthesis, then levels off slightly, and then increases steeply to left parenthesis 7 comma 1500 right parenthesis.
B. A coordinate plane shows the x-axis, labeled as Number of Minutes, ranging from 0 to 10 in increments of 1, and the y-axis, labeled as Number of Meters, ranging from 0 to 1600 in increments of 100. A straight line connects the following two plotted points: left parenthesis 0 comma 0 right parenthesis and left parenthesis 7 comma 1,500 right parenthesis.
C. A coordinate plane shows the x-axis, labeled as Number of Minutes, ranging from 0 to 10 in increments of 1, and the y-axis, labeled as Number of Meters, ranging from 0 to 1600 in increments of 100. A curve connects 2 plotted points. The coordinates of a plotted closed circle are left parenthesis 0 comma 0 right parenthesis, and a second closed circle is plotted at left parenthesis 7 comma 1500 right parenthesis. An upward concave curve connects the two points. The curve passes through left parenthesis 6 comma 800 right parenthesis.
D. A coordinate plane shows the x-axis, labeled as Number of Minutes, ranging from 0 to 10 in increments of 1, and the y-axis, labeled as Number of Meters, ranging from 0 to 1600 in increments of 100. The coordinates of a plotted closed circle are left parenthesis 0 comma 0 right parenthesis, and a second closed circle is plotted at left parenthesis right 7 comma 1,500 parenthesis. A downward concave curve connects the two points. The curve passes through left parenthesis 1 comma 600 right parenthesis, left parenthesis 3 comma 1200 right parenthesis, and left parenthesis 5 comma 1400 right parenthesis.
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1. B. Linear Function 1 has the greater rate of change, with a rate of change equal to 15 while Linear Function 2 has a rate of change equal to 1.
2. D. Linear Function 2 has the lesser initial value, with an initial value equal to $40 while Linear Function 1 has an initial value equal to $45.
3. A. A coordinate plane with four quadrants shows the x and y axes ranging from negative 8 to 8 in increments of 1. An upward line with arrows on both the ends passes through the first, fourth, and third quadrants. The line intersects the x-axis at left parenthesis 0.3 comma 0 right parenthesis and the y-axis at left parenthesis 0 comma negative 1 right parenthesis. Values are approximate.
4. B. A coordinate plane shows the x-axis, labeled as Number of Minutes, ranging from negative 2 to 30 in increments of 2, and the y-axis, labeled as Page Number, ranging from negative 5 to 100 in increments of 5. A ray extends from a plotted point. The coordinates of the plotted closed circle are left parenthesis 0 comma 15 right parenthesis. An upward slanting arrow extends from the plotted point and passes through left parenthesis 30 comma 75 right parenthesis.
5. A. A coordinate plane shows the x-axis, labeled as Number of Minutes, ranging from 0 to 10 in increments of 1, and the y-axis, labeled as Number of Meters, ranging from 0 to 1600 in increments of 100. A curve with a closed circle at both the ends is shown. The coordinates of a plotted closed circle are left parenthesis 0 comma 0 right parenthesis. An upward curve extends from this point and increases steeply to left parenthesis 4 comma 900 right parenthesis, then levels off slightly, and then increases steeply to left parenthesis 7 comma 1500 right parenthesis.
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