Question

Determine whether the function f(x) = -2x - 5x is even, odd, or neither.

Answer 1

Answer: odd

Explanation:

A function is even if for any input value x and -x there is the same output value y. In other words, a function is even if:

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

A function is odd if it is true that:

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

Then we must test if
`f(-x) = f(x)` for the function:
`f(x)=-2x - 5x`

`f(-x)=-2(-x) - 5(-x)`

`f(-x)=2x + 5x`

So
`f(-x) \\eq f(x)`

The function is not even

Now we must test if
`f (-x) = -f (x)` for the function.

`f(-x)=-2(-x) - 5(-x)`

`f(-x)=2x + 5x`

`f(-x)=-(-2x -5x)` and
`f(x)=-2x - 5x`

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

Finally the function is odd