Question

priya is running once around the track. the graph shows her time given how far she is from her starting point.a. what was her farthest distance from her starting point?b. estimate how long it took her to run around the track.c. estimate when she was 100 meters from her starting point.d. estimate how far she was from the starting line after 60 seconds.e. is priyas time a function of her distance from her starting point? explain how you know.

Explanation:

Step1: Identify max distance on x-axis

Look at the rightmost point of the graph's x-axis (distance).

Step2: Find total time from graph

The end of the top curve gives total lap time.

Step3: Match 100m to time values

Locate 100m on x-axis, find corresponding y-values (time) on both curves.

Step4: Match 60s to distance value

Locate 60s on y-axis, find corresponding x-value (distance) on the top curve.

Step5: Check function definition

A function has one output per input; check if 1 distance has 2 times.

Answer:

a. 200 meters
b. 72 seconds
c. At approximately 20 seconds (when moving away from the start) and 50 seconds (when returning to the start)
d. Approximately 50 meters
e. No, Priya's time is not a function of her distance from the starting point. For a single distance value (e.g., 100 meters), there are two different corresponding time values, which violates the definition of a function (each input must have exactly one output).