Graphs of Piecewise Linear Functions Define appropriate quantities from a situation, choose and...
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Graphs of Piecewise Linear Functions Define appropriate quantities from a situation, choose and interpret the scale and the origin for the graph, and graph
Graphs of Piecewise Linear Functions Define appropriate
quantities from a situation, choose and interpret the scale and the
origin for the graph, and graph the piecewise linear function.
Slide 2
Learning Goal 2 (HS.N-Q.A.1, 2, 3): The student will be able to
use units to solve multi-step contextual problems.
Slide 3
Video Watch the following video. Your goal is to be able to
describe the motion of the man in words. Describe the motion of the
man in the video. Describe the man in terms of change in elevation
of the man and the amount of time.
Slide 4
VideoAnalyze How high do you think the man was at the top of
the stairs? How did you estimate that elevation? Were there
intervals of time when his elevation wasnt changing? Was he still
moving? Did his elevation ever increased? When?
Slide 5
VideoGraph How should we label the vertical axis? What
measurement should we choose (feet or meters)? How should we label
the horizontal axis? What unit of measure should we choose? Should
we measure the mans elevation to his feet or to his head on the
graph? The man starts at the top of the stairs. Where would that be
located on the graph? Draw the graph.
Slide 6
What the graph could look like. 2 4 6 8 10 12 14 16 Elevation
(feet) Time (Seconds) Elevation vs. Time Graph Man in Green
Jacket
Slide 7
Elevation Vs. Time Graph #2 With a partner describe what this
person might have been doing.
Slide 8
What is happening in the story when the graph is increasing?
Decreasing? Staying constant? What does it mean for one part of the
graph to be steeper than another part? How does slope of each line
segment relate to the context of the persons elevation?
Slide 9
Is it possible that this is a graph of a person moving up and
down a vertical ladder? Is it possible for someone walking on a
hill to produce this graph? What was the average rate of change of
the persons elevation between time 0 minutes and time 4 minutes? 10
/ 4 feet per minute or 2.5 feet per minute.
Slide 10
What type of equation (s) would be required to create this
graph?
Slide 11
Piecewise Linear Function Definition: Given non-overlapping
intervals on the real number line, a (real) piecewise linear
function is a function from the union of the intervals on the real
number line that is defined by (possible different) linear
functions on each interval. All the graphs we studied today are
Piecewise Linear Functions. Here are a few more:
Slide 12
union of intervals.. Piecewise linear functions are defined
over an interval of time shown on the horizontal axis. List those
time intervals. (0 to 2) (2 to 5) (5 to 7)