Determine whether the function ƒ(x) = –2x3 – 5x is even, odd, or neither. neither odd even

For this case we have the following function:
 
 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:
 
 Rewriting:
 

 Therefore, according to the definition, the function is odd.

 
 
 The function is odd

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