Question

Determine algebraically whether the function is even, odd, or neither even nor odd.

f(x) = -3x

Answer 1

\[f(–x) = –f(x)\]
The function will be odd if it obeys what I wrote above.
\[f(–x) = f(x)\]
The function is even if it obeys what I wrote above.
If the function does obey both of them, then it's neither.
SO...
\[f(x)=-3x\]
\[f(-x)=-3(-x)\]
\[=3x\]
So it's not even.
Let's Try it to see if the function is even.
\[-f(x)=-(-3x)\]
\[=3x\]
Therefore,
\[f(-x)=-f(x)\]
Thus, it is odd...