Question

Give an example of an odd function and explain algebraically why it is odd. (3 points)

Answer 1

See below

Explanation:

In an odd function f(-x) will equal -f(x).

An example is f(x) = x^3:-

f(-x) = (-x)^3 and -f(x) = -x^3:-

(-x)^3 = -x * -x * -x = -x^3.

Answer 2

Answer:
`f(x)=5x^(3)-x`

Explanation:

1. By definition, algebraically, a function is odd when:

`-f(x)=f(-x)`

2. Therefore, if you have the following function:

`f(x)=5x^(3)-x`

You can know if it is odd by substituting
`x=-x`:

`f(-x)=5(-x)^(3)-(-x)`

`f(-x)=-5x^(3)+x`

3.
`-f(x)` is:

`-f(x)=-5x^(3)+x`

4. Then, as
`-f(x)=f(-x)` it is odd