Determine Algebraically Whether the Function Is Even, Odd, or Neither $$f ( x ) = 2 x ^ { 3 } - 4$$

question 194

Multiple Choice

Determine algebraically whether the function is even, odd, or neither.
- $$f ( x ) = 2 x ^ { 3 } - 4$$

• A) even
• B) odd
• C) neither

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Definitions:

Universal Instantiation

A principle in logic that allows for the deducing of a statement about a specific instance from a general statement that applies to all instances.

Universal Generalization

A form of deductive reasoning that concludes a general statement is true for all instances based on the observation of particular instances.

Quantifier Negation

The process of negating the quantifiers in a statement, such as changing "all" to "not all" or "some" to "none".

Existential Generalization

A logical operation that infers the existence of at least one member of a domain that satisfies a certain property from a specific case.