Comment on Activity 4

If the function graphed in Figure A1 is even, then the value assigned to ${\displaystyle -a}$ is the same as the value assigned to ${\displaystyle a}$, i.e., ${\displaystyle \text{(}-a,b\text{)}}$ is on the graph. This means that the portion of the graph on the left side of the ${\displaystyle y}$-axis may be obtained from the portion on the right by rotating around the ${\displaystyle y}$-axis. On the other hand, if the function is odd, then the value assigned to ${\displaystyle -a}$ is the negative of the value assigned to ${\displaystyle a}$, i.e., ${\displaystyle \text{(}-a,-b\text{)}}$ is on the graph. This means that the portion of the graph on the left side of the ${\displaystyle y}$-axis may be obtained from the portion on the right by rotating around the ${\displaystyle y}$-axis and then rotating about the ${\displaystyle x}$-axis (or vice versa). See Figures A2 and A3 for the even and odd cases, respectively.

Figure A2   An even function	Figure A3   An odd function