Changing Behavior of Open Graphs

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GR. 9-12

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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