Question: Test algebraically whether f(x) equals negative 6 is even, odd, or neither even nor odd. Is this function even, odd, or neither even nor odd?
1. **State the problem:** We need to determine if the function $$f(x) = -6$$ is even, odd, or neither.
2. **Recall definitions:**
- A function $$f$$ is **even** if $$f(-x) = f(x)$$ for all $$x$$.
- A function $$f$$ is **odd** if $$f(-x) = -f(x)$$ for all $$x$$.
3. **Evaluate $$f(-x)$$:**
Since $$f(x) = -6$$ is a constant function, $$f(-x) = -6$$.
4. **Check evenness:**
Compare $$f(-x)$$ and $$f(x)$$:
$$f(-x) = -6$$ and $$f(x) = -6$$
Since $$f(-x) = f(x)$$, the function satisfies the condition for being even.
5. **Check oddness:**
Compare $$f(-x)$$ and $$-f(x)$$:
$$f(-x) = -6$$ and $$-f(x) = -(-6) = 6$$
Since $$f(-x) \neq -f(x)$$, the function is not odd.
6. **Conclusion:**
The function $$f(x) = -6$$ is **even**.
**Final answer:** B. Even