sketching a piecewise function. piecewise the function has different qualities at different...
DESCRIPTION
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.TRANSCRIPT
Lesson 1.6Sketching a Piecewise Function
PiecewiseThe function has different qualities at
different intervals.
time
dist
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.
time
dist
time
dist
time
dist
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.
time
dist
time
dist
time
dist
Speed vs. TimeThe 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…
time
dist
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.
time
speed
time
speed
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 FunctionsIdentify the two variables that are being
compared.Label your axes
X-axis – independent variableY-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
Example 4 continuedHow 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?