The question asks to determine the domain of the function $f(x) = x^4 + 4x$.

To determine the domain of the function:

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

• The function $f(x) = x^4 + 4x$ is a polynomial.
• Polynomial functions are defined for all real numbers.

So, the domain of $f(x)$ is all real numbers, which is $(-\infty, \infty)$.

Correct Answer:

• Option B: $(-\infty, \infty)$

Would you like further details or have any questions? Here are 5 related questions for further exploration:

1. What is the range of the function $f(x) = x^4 + 4x$?
2. How do you find the critical points of the function $f(x) = x^4 + 4x$?
3. What is the behavior of the function $f(x) = x^4 + 4x$ as $x$ approaches infinity and negative infinity?
4. How would you determine the intervals of increase and decrease for the function $f(x) = x^4 + 4x$?
5. What are the local maxima and minima of the function $f(x) = x^4 + 4x$?

Tip: For polynomial functions, the domain is typically all real numbers unless there's a division by zero or square root of a negative number involved.