Question

is the function m(x) = -3x⁴ - 2 even, odd, or neither? even odd neither

Explanation:

Step1: Recall the definitions

A function \( m(x) \) is even if \( m(-x) = m(x) \) for all \( x \) in the domain. A function is odd if \( m(-x) = -m(x) \) for all \( x \) in the domain.

Step2: Compute \( m(-x) \)

Given \( m(x) = -3x^4 - 2 \), substitute \( -x \) for \( x \):
\( m(-x) = -3(-x)^4 - 2 \)
Since \( (-x)^4 = x^4 \) (because any even power of a negative number is positive), we have:
\( m(-x) = -3x^4 - 2 \)

Step3: Compare \( m(-x) \) with \( m(x) \) and \( -m(x) \)

We see that \( m(-x) = -3x^4 - 2 = m(x) \). Now check \( -m(x) \):
\( -m(x) = -(-3x^4 - 2) = 3x^4 + 2 \), which is not equal to \( m(-x) \).

Since \( m(-x) = m(x) \), the function is even.

Answer:

even