1.2    Symmetry

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                                                                                                             http://youtu.be/BNKUzSohiD8 

1-4. Graph the following functions.


1.

 

                               


2.

            

                                      


3.

     

                                           


4.

                                               


5. Find the formula for graph of funstion.

   

                                                      

    

6-10. Graph the functions in Exercises 6-10. What symmetry, if any, do the graphs have? Specify the intervals over where the function is increasing and the intervals where it is decreasing.


6.

                                                       

   (i) symmetric about the origin, and

   (ii) decreasing on


7.

  http://matrix.skku.ac.kr/cal-lab/cal-1-2-7.html

plot(-1/x, -2, 2, exclude=[0], ymax=5, ymin=-5)

                                                   

   (i) symmetric about the origin,

   (ii) increasing on ,

   (iii) increasing on


8.

                                                           

   (i) symmetric with respect to the -axis,

   (ii) decreasing on ,

   (iii) increasing on


9. (similar to 6)

                                                               

   (i) symmetric about the origin,

   (ii) increasing on ℝ


10.

                                                                    

   (i) it has no symmetries,

   (ii) decreasing on


11-16. Determine whether the given function is even, odd, or neither. Give reasons for your answer.


11.

 Since for all , is even function.


12.

 Since for all , is an even function.


13.

 Since for all , is an odd function.


14.

 Since for all , is an even function.


15.

 

     .

     This means and also . Hence is neither odd, nor even function.


16.

 . is neither odd, nor even function.

http://matrix.skku.ac.kr/cal-lab/cal-1-2-Rational-Fts.html 

# [Note] Sage code for Graph of rational functions:

plot((1+x^2)/((x-1)*(x+1)*(x-2)), -3, 4, exclude=[-1, 1, 2], ymax=20, ymin=-20, figsize=6)


                                                

Playing Math Game at ICME12 (2012)

 

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