Question

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

Answer 1

Answer: odd

Step-by-step 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 $f(-x) \neq f(x)$

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