Question

Jessie walked three miles in hour 1 of a four hour walk-a-thon. She then decided to keep track of her speed and

distance walked each of the three remaining hours. The piecewise function below estimates the distance she travels
(in miles).
f(x)=
{
5(x-1) +3,
2(x-2) +8,
3(x-3)+10,
1 2 3 a. On which interval is Jessie walking the fastest?
b. f(4)= 13. Explain what it means in terms of the context of the story.

Answer 1

In the first hour, Jessie is walking the fastest. f(4)=13 means that in the fourth hour, Jessie traveled a distance of 13 miles.

Step-by-step explanation:

a. To determine the interval in which Jessie is walking the fastest, we need to compare the rates of change of the distance function in each interval. The rates of change are given by the slopes of the linear functions within each interval.

The interval with the steepest slope will indicate that Jessie is walking the fastest. Comparing the slopes, we can see that the slope of the first interval, 5, is greater than the slopes of the other intervals, 2 and 3.

Therefore, Jessie is walking the fastest in the first interval.

b. To find f(4), we substitute x=4 into the appropriate function within the piecewise function. In this case, Jessie is in the third interval, so we use the function 3(x-3)+10. Substituting x=4, we have f(4)=3(4-3)+10=3+10=13. In terms of the story, this means that in the fourth hour of the walk-a-thon, Jessie traveled a distance of 13 miles.