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.

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