Question

Question #4e641

Answer 1

This is an odd function.

Explanation:

To check if a function `f(x)` is odd or even (or neither) you have to calculate `f(-x)` and compare the calculated value with `f(x)`.

• If `f(-x)=f(x)` then `f(x)` is even,

• if `f(-x)=-f(x)` then `f(x)` is odd.

Here we have:

`f(x)=x^3+7x`

`f(-x)=(-x)^3+7*(-x)`

`f(-x)=-x^3-7x`

We see that the value is an opposite expression to `f(x)`.

`f(-x)=-f(x)`, so the function is odd

Other way to see if the function is even or odd is to look at the function's graph.

• if the graph is symetrical according to `Y` axis then the function is even.Example: `y=x^2+2`

graph{x^2+2 [-10, 10, -5, 5]}

• If the graph is symetrical according to the origin `(0,0)` then it is odd. Example: `x^3+7x`

graph{x^3+7x [-3, 3, -50, 50]}