The given function $f(x) = \frac{1}{4}x - \frac{1}{7}$ is a linear function.

For linear functions, the domain is typically all real numbers because they are defined for every value of $x$.

So, the domain of the function $f(x) = \frac{1}{4}x - \frac{1}{7}$ is:

$\text{Domain} = \mathbb{R} \quad \text{or} \quad (-\infty, \infty)$

Would you like more details or have any questions?

Here are 5 related questions:

1. What is the range of the function $f(x) = \frac{1}{4}x - \frac{1}{7}$?
2. How do you determine the slope of the function from its equation?
3. What is the y-intercept of the function $f(x) = \frac{1}{4}x - \frac{1}{7}$?
4. How would you graph the function $f(x) = \frac{1}{4}x - \frac{1}{7}$?
5. Can the domain of a linear function ever be restricted?

Tip: The domain of a function refers to all possible input values (x-values) that the function can accept without causing any mathematical issues, such as division by zero or taking the square root of a negative number.