Question

Four functions are given below. Either the function is defined explicitly, or the entire graph of the function is shown.

For each, decide whether it is an even function, an odd function, or neither.

Answer 1

Explanation:

even function is symmetric along the y-axis

the y-axis acts like a mirror

f(x) = f(-x) for any real x

odd function is similar to even function except

one side is up-side-down. (rotational symmetric by 180 degree)

odd function is nice property since the definite integral

from -a to a always equals to 0

f(x) = -f(-x) for any real x

top-left:

even

top-right:

odd

bottom-left:

Neither

bottom-right:

odd