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 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.
Image with alt text: 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.
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.
Image with alt text: 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.
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.
Image with alt text: 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.
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.
Image with alt text: 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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1 answer
To select the graph that accurately reflects Jasmine’s running pattern, we must consider the description of her speed throughout the race:
Starts out fast: This indicates that initially, the distance increases rapidly.
Slows down toward the middle: This suggests that the increase in distance becomes less steep in the middle segment of her run.
Finishes by sprinting: Finally, this implies that at the end of the race, her speed increases again, making the distance increase rapidly once more.
Based on these observations, the most suitable graph will depict a curve that rises steeply at the beginning, flattens out in the middle, and then steepens again towards the end.
Looking through the options:
The first graph (downward concave) does not show the initial speed up, only a slowdown and then a turnaround, which does not match the description.
The second graph (straight line) assumes a constant speed, which contradicts the varying speeds described.
The third graph (upward concave) suggests increasing speed overall, which does not accurately represent Jasmine's running pattern as it doesn't show her slowing down in the middle.
The fourth graph (a curve that initially rises steeply, then slightly levels off, and then rises steeply again) matches perfectly with the description of Jasmine’s running pattern as it reflects the initial fast start, the slowdown, and the final sprint to the finish.
Therefore, the correct choice is the fourth graph, which maintains the qualitative features of Jasmine’s performance throughout the race.
