Sketching a Piecewise Function

Piecewise The function has different qualities at different intervals.

Example 1: Match the description with the graph. George started at his friend’s house and began walking home. After a few blocks, he realized he forget his cell phone and hurried back to his friend’s house to pick it up. After grabbing his phone, he immediately began running back home because he was afraid he was going to be late. Unfortunately he got stuck for a little while trying to cross the busy street. After crossing the busy street, he decided to walk the rest of the way home instead of running. Which graph shows George’s distance from home in terms of time? A.B.C.

Example 2: Match the description with the graph. Joanne started running a marathon as fast as she could. During the first few minutes she gradually slowed down until she stopped at about the half way point of the marathon. She had to take a long break sitting on a bench because she had run too fast. She then ran at a slower constant speed until the end of the marathon where she promptly collapsed. Which graph shows Joanne’s distance run in terms of time? A.B.C.

Speed vs. Time The same situations in terms of speed would give different results. George started at his friend’s house and began walking home. After a few blocks, he realized he forget his cell phone and hurried back to his friend’s house to pick it up. After grabbing his phone, he immediately began running back home because he was afraid he was going to be late. Unfortunately he got stuck for a little while trying to cross the busy street. After crossing the busy street, he decided to walk the rest of the way home instead of running. Which graph shows George’s speed in terms of time?

This graph doesn’t make sense anymore…

Which graph shows George’s speed in terms of time? George started at his friend’s house and began walking home. After a few blocks, he realized he forget his cell phone and hurried back to his friend’s house to pick it up. After grabbing his phone, he immediately began running back home because he was afraid he was going to be late. Unfortunately he got stuck for a little while trying to cross the busy street. After crossing the busy street, he decided to walk the rest of the way home instead of running. A B

Example 3: A child climbed slowly up a slide, sat at the top of a little while, and then quickly slid down. Which graph shows height off the ground versus time? Which graph shows speed versus time?

Sketching Piecewise Functions Identify the two variables that are being compared. Label your axes X-axis – independent variable Y-axis – dependent variable Graph the situation

Example 4: Sketch the following function of the cat’s speed in terms of time. A cat is sitting on a pillow across the room watching the cicadas climb up the sliding glass door. The cat sits perfectly still for several moments before quickly charging towards the sliding glass door where she slams into it coming to a halt. After pausing a moment to realize the cicadas were scared away, the cat slowly slinks to the middle of the room to wait on the next cicada to show up.

Example 4 continued

How would the graph look if you were to represent the function of the cat’s distance from the sliding glass door in terms of time?