Mastery Check Solutions

Show What You Know

A novice hiker’s loop-trail hike was recorded using a GPS device. Because the trail is a loop, the start and end is at the same location where the distance is zero. 

• • The first 3 miles of the hike took one hour.
  • Then the hiker took a 10 minute break.
  • The next mile took one hour, as this part of the trail was very steep. 
  • The hiker’s next break was for 20 minutes.
  • The last part of the loop-trail took 100 minutes.

1. Use the information provided to graph the scenario.

An expert hiker took the same loop-trail. Their GPS tracked them in the same way as the novice hiker. 
$e\left(x\right)=\left\{\begin{array}{ll}6x& \mathrm{if} 0\le x\le 0.5\\ 2\left(x–0.5\right)+3& \mathrm{if} 0.5<x\le 1\\ –5\left(x–1\right)+4& \mathrm{if} 1<x\le 1.8\end{array}\right.$

3. What is the total distance that both hikers completed?
   $3+1+4=8 \mathrm{miles}$

4. What is the time difference between the hikes of the novice and expert?

   $$\begin{gathered} 4 \mathrm{hr} 10 \mathrm{minutes}–1 \mathrm{hour} 48 \mathrm{minutes}=250 \mathrm{minutes}–108 \mathrm{minutes}=142 \mathrm{minutes} \\ 142 \min (1 \mathrm{hr}/60 \min )=2 \mathrm{hours} 22 \mathrm{minutes} \end{gathered}$$

5. What does a negative rate of change mean for both hikers?
   This means that they are heading back toward the start of the trail. 

Say What You Know

In your own words, talk about what you have learned using the objectives for this lesson and your work on this page.

Note

Restate the objectives of the lesson in your own words. If you are unable to restate the lesson objectives, go back and reread the objectives and then explain them.

• Graph piecewise functions, including scenarios, over the given intervals.
• Write piecewise functions with intervals given a graph.
• Find the rate of change over a specified interval.