Question

Determine whether the function f(x) = 4x3 is even or odd.

The function is even because f(−x) = f(x).
The function is odd because f(−x) = f(x).
The function is even because f(−x) = −f(x).
The function is odd because f(−x) = −f(x).

Answer 1

To determine whether the function \( f(x) = 4x^3 \) is even or odd, we need to evaluate \( f(-x) \) and compare it to \( f(x) \) and \( -f(x) \).

1. **Calculate \( f(-x) \)**:
\[
f(-x) = 4(-x)^3 = 4(-x^3) = -4x^3
\]

2. **Compare \( f(-x) \) with \( f(x) \) and \( -f(x) \)**:
- \( f(x) = 4x^3 \)
- \( -f(x) = -4x^3 \)

From our calculations:
- We see that \( f(-x) = -4x^3 = -f(x) \).

Since \( f(-x) = -f(x) \), we conclude that the function \( f(x) = 4x^3 \) is **odd**.

Thus, the correct statement is:
- **The function is odd because \( f(-x) = -f(x) \)**.