SKKU-Calculus-Sec-1-2 by SGLee

1.2    Symmetry

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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.

(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.

(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.

Playing Math Game at ICME12 (2012)