Questions: Determine if the following function is even, odd, or neither. n(x)=-4x-2

Solution Steps

To determine if a function is even, odd, or neither, we need to check the following:

1. A function \( f(x) \) is even if \( f(x) = f(-x) \) for all \( x \).
2. A function \( f(x) \) is odd if \( f(-x) = -f(x) \) for all \( x \).
3. If neither condition is satisfied, the function is neither even nor odd.

For the given function \( n(x) = -4|x| - 2 \), we will:

1. Compute \( n(-x) \).
2. Compare \( n(x) \) and \( n(-x) \) to determine if the function is even, odd, or neither.

We are given the function \( n(x) = -4|x| - 2 \).

To determine if the function is even, odd, or neither, we first compute \( n(-x) \): \[ n(-x) = -4|-x| - 2 = -4|x| - 2 = n(x) \]

Since \( n(-x) = n(x) \), we conclude that the function satisfies the condition for being even.

Final Answer