1.2 Symmetry

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) decreasing 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

10.

(i) it has no symmetries,

(ii) decreasing on

11-16.Check whether the functions 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 or even function.

16.

. is neither odd or even function.