For this case we have the following function:
[tex]ƒ (x) = -2x ^ 3 - 5x
[/tex]
By definition, we have to:
A function is even if, for each x in the domain of f, f (- x) = f (x). The even functions have reflective symmetry through the y-axis.
A function is odd if, for each x in the domain of f, f (- x) = - f (x). The odd functions have rotational symmetry of 180º with respect to the origin.
Evaluating f (-x) we have:
[tex]f (-x) = -2 (-x) ^ 3 - 5 (-x)
[/tex]
Rewriting:
[tex]f (-x) = - (- 2 (x) ^ 3 - 5 (x))
f (-x) = - f (x)[/tex]
Therefore, according to the definition, the function is odd.
Answer:
[tex]f (-x) = - f (x)
[/tex]
The function is odd
