For each equation below, determine if the function is Odd, Even, or Neither
Select an answer
Select an answer
Select an answer
Question Help:
Submit Question

An even function satisfies the condition , while an odd function satisfies . For , if you substitute , you’ll observe that it remains unchanged when squared, thus making it even. On the other hand, the function can be analyzed by plugging in , and you’ll find it does not return the original value or the negative; hence, it’s neither. Lastly, for , it’s an interesting case. If you input , the function reflects symmetry about the y-axis, revealing its even nature.

To better understand even and odd functions, consider how they graphically behave. Even functions exhibit symmetry around the y-axis—think of a snowy mountain peak—while odd functions are symmetric around the origin, reminiscent of spinning like a ballerina. It’s fun to graph both types to visually grasp these properties!