Changing Behavior of Open Graphs
Skill:
Describe the intervals for which a function is increasing or decreasing.
Changing Behavior of Open Graphs
Discover what it means for intervals of a graph to be increasing, decreasing or constant.
Open-ended question 1
What does it mean for a graph to be increasing over an interval? Decreasing? Constant?
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Open-ended question 2
What can a graph look like when it is ONLY increasing? Decreasing? Constant?
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Open-ended question 3
Is it possible for a graph to be both increasing and decreasing?
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Open-ended question 4
Is it possible for a graph to be neither increasing nor decreasing?
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Open-ended question 5
Can two intervals of a graph look different and yet both be increasing?
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Open-ended question 6
What happens when two adjacent intervals of the graph exhibit the same behavior?
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Open-ended question 7
Move the points so that part of the graph looks like a quadratic function. Over what intervals is it increasing, decreasing, or constant?
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Open-ended question 8
Could the graph of an exponential function (like ) have intervals that are increasing, decreasing, or constant?
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Open-ended question 9
How does the behavior of a quadratic function compare to the behavior of an exponential function?
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Open-ended question 10
Can a function be increasing, decreasing or constant at a single point? Why or why not?
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Prerequisite Resources
