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Dynamic Graphs 2

Activity 1

            Recall our last dynalab activity.  Near the end of the activity, you were guessing the function that was represented by a given dyangraph.  Please do the same with the dynagraphs below.  Significant characteristics to guide your thought process are:

• How is the output changing as the input is changing? Is the rate of change constant or not?

• What is the initial value of the output, i.e. what is the value of the output when the input = 0?

• What is the value of the output when the input is 1?

• Does every possible input have an output?

• What is the set of all possible outputs?  Then entire real number line?  Just the positive real numbers?  Just the negative real numbers?

            1.  dynaguess3.1  1

            2.  dynaguess3.1  2

            3.  dynaguess3.1  3

            4.  dynaguess3.1  4

            5.  dynaguess3.1.  5

Activity 2

Now we will expand our repertoire of functions.  This dynagraph represents a function that is neither linear nor exponential.  Play around with it bit and answer the following questions. 

• How is the output changing as the input is changing? Is the rate of change constant or not? Does the output change more slowly or more quickly than the input?

• What is the initial value of the output, i.e. what is the value of the output when the input = 0?  When the input = 1?   What input gives an output value of 0? 

• What is the value of the output when the input is 1?

• Does every possible input have an output?

• What is the set of all possible outputs?  Then entire real number line?  Just the positive real numbers?  Just the negative real numbers?

Discuss with a colleague what function this might represent.  Make a table of values to help in your decision.  Then check your conjecture by clicking on the “Show Function” button.

Guess the function represented by each of the following. Hint:  each are logarithmic functions.  You need to decide upon the base.

6.    dynaguess3.1  6

7.    dynaguess3.1  7

8.    dynaguess3.1  8

Activity 3

Your job in this activity is to match the dynagraph with its function from the list at the right.   No fair clicking on the “Check Function” buttons until you’ve guessed them all.

9.    dynaguess3.1  9                                           A.   

10.   dynaguess3.1  10                                         B.   

11.   dynaguess3.1  11                                          C.    

12.   dynaguess3.1  12                                          D.   

13.   dynaguess3.1  13                                         E.   

14.   dynaguess3.1  14                                         F.  

The remaining activities related to functions not studied in FMVI.  We list them here for your further enrichment.  Enjoy!

Activity 4

            Now, experiment with this dynagraph. 

           If you move the inputs around too quickly, the behavior of the outputs seems totally wild, so move the inputs very slowly as you answer the following questions.

• How is the output changing as the input is changing?   Note particularly the behavior as you move the input slowly to the right, so that the input is getting larger and larger. What happens to the output?     Then note a different behavior as you move the input close to 0 from the right side. What might be causing this seemingly strange behavior? 

• What happens when you try to find the initial value of the output, i.e. what happens to the output when the input gets very close to 0?  Why might this happen?

• What is the value of the output when the input is 1?

• Does every possible input have an output?

• What is the set of all possible outputs?  Then entire real number line?  Just the positive real numbers?  Just the negative real numbers?

Guess the function represented by each of the following.

15.  dynaguess3.1  15

16.  dynaguess3.1  16

17.  dynaguess3.1  17   

Activity 5

   Last  one.  Experiment with this dynagraph and answer the usual questions, listed below

   for your convenience.   

• How is the output changing as the input is changing? Is the rate of change constant or not? Does the output change more slowly or more quickly than the input?

• What is the initial value of the output, i.e. what is the value of the output when the input = 0?

• What is the value of the output when the input is 1?

• Does every possible input have an output?

• What is the set of all possible outputs?  Then entire real number line?  Just the positive real numbers?  Just the negative real numbers?

Guess the function represented by each of the following.

 18.  dynaguess3.1  18

 19.  dynaguess3.1  19

 10.  dynaguess3.1  20   

 21.  dynaguess3.1  21

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