Based on the data, the students in Mr. Lastorka's class determine the exact equation involving Watts, x, and total distance from start, y . They call the function y = f(x). Mr. Lastorka then instructs his class to reflect y = f(over the x-axis. He challenges each student to determine the new function and what it would mean from a physics perspective. Four student pairs gave their answers below. Who is correct, and for what reasons?
A. Charles and Shannon, who identify the new equation as y = -2x and explain that the new graph indicates that the car is still moving forward at the same rate as before.
B. Michael and Lauren, who identify the new equation as y = -2x and explain that the new graph indicates the car is now moving in reverse at the same rate as before.
C. Matthew and Karen, who identify the new equation as y = 2-x and explain that the new graph indicates that the car is now moving forward more rapidly than before.
D. Andy and Joanie, who identify the new equation as y = 2-x and explain that the new graph indicates that the car is no longer moving in any direction.
Answer:B
Based on the data, the students in Mr. Lastorka's class determine the exact equation involving Watts, x, and total distance from start, y . They call the function y = f(x). Mr. Lastorka then instructs his class to reflect y = f(over the x-axis. He challenges each student to determine the new function and what it would mean from a physics perspective. Four student pairs gave their answers below. Who is correct, and for what reasons?
A. Charles and Shannon, who identify the new equation as y = -2x and explain that the new graph indicates that the car is still moving forward at the same rate as before. B. Michael and Lauren, who identify the new equation as y = -2x and explain that the new graph indicates the car is now moving in reverse at the same rate as before. C. Matthew and Karen, who identify the new equation as y = 2-x and explain that the new graph indicates that the car is now moving forward more rapidly than before. D. Andy and Joanie, who identify the new equation as y = 2-x and explain that the new graph indicates that the car is no longer moving in any direction.
Explanation: B If the original graph is reflected across the x-axis, the x-values will remain the same but the y-values will switch signs. Since the y-axis represents distance from start, negative y-values means that the car is now going in reverse. The only answer that matches this information is (B).