Question

(1 point)
Responses

even
even

odd
odd

neither

Answer 1

Determine whether the function f(x) = 9x^4 + 4 is even, odd or neither

Answer 2

It seems like you're presenting a set of responses that could relate to whether certain numbers or expressions are even, odd, or neither. If you provide more context or specific numbers or expressions, I can help clarify or give a more thorough analysis!

Answer 3

To determine whether the function \( f(x) = 9x^4 + 4 \) is even, odd, or neither, we can use the definitions of even and odd functions:

- **Even function**: A function \( f(x) \) is even if \( f(-x) = f(x) \) for all \( x \).
- **Odd function**: A function \( f(x) \) is odd if \( f(-x) = -f(x) \) for all \( x \).

Let's calculate \( f(-x) \):

\[
f(-x) = 9(-x)^4 + 4
\]

Since raising a number to an even power negates the effect of the negative sign, we have:

\[
(-x)^4 = x^4
\]

Therefore, we can rewrite \( f(-x) \):

\[
f(-x) = 9x^4 + 4
\]

Now we can compare \( f(-x) \) with \( f(x) \):

\[
f(x) = 9x^4 + 4
\]
\[
f(-x) = 9x^4 + 4
\]

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

**Conclusion**: The function \( f(x) = 9x^4 + 4 \) is an even function.