Determine whether the following function is even, odd or neither: (Justify your answer in either work or words)
f(x) = 2x3 – 3x

Question

Determine whether the following function is even, odd or neither: (Justify your answer in either work or words)
                f(x) = 2x3 – 3x

mr.math · Answer

An even function is a function that satisfies $f(-x)=f(x)$.
An odd function is a function that satisfies $f(-x)=-f(x)$.

mr.math · Answer

$$f(-x)=2(-x)^3-3(-x)=-2x^3+3x=-(2x^3-3x).$$

mr.math · Answer

Based on the definitions I gave, what can you conclude?

mr.math · Answer

Try to compare f(-x) to f(x)!

mr.math · Answer

Can't you see that $f(-x)=-f(x)$?

anonymous · Answer

so it would be negative, correct?

mr.math · Answer

What would be negative?

anonymous · Answer

I'm sorry, I mean positive! The function would be positive?

mr.math · Answer

Being even and odd is not related to being positive or negative, it doesn't really matter. All you need is to use the definition. For the function you gave, we found that f(-x)=-f(x), and this what an  odd function is, thus f(x) is odd.