Determine weather the function below is an even function, an odd function, or both or neither f (x) = 3/4x

Hello!

Even functions are functions that are symmetric with respect to the y-axis. It can be proved algebraically by determining if f (-x) = f (x).

Odd functions are functions that are symmetric with respect to the origin. It can also be proved algebraically by determining if f (-x) = - f (x).

1. f (-x) = f (x) | Even function

f (-x) = 3/4 (-x) = - 3/4x

f (x) = 3/4x

-3/4x is not equal to 3/4x

2. f (-x) = - f (x) | Odd function

f (-x) = 3/4 (-x) = - 3/4x

-f (x) = - 3/4x

-3/4x is equal to - 3/4x

Therefore, the function, f (x) = 3/4x, is an odd function.