To determine the value of the function $f(x) = -4x + 7$ at $x = 0$, we simply substitute $x = 0$ into the function:

$f(0) = -4(0) + 7$

Simplifying:

$f(0) = 0 + 7 = 7$

Thus, the value of the function at $x = 0$ is $\boxed{7}$.

Would you like further explanation or clarification?

Here are some related questions:

1. How would the function $f(x) = -4x + 7$ change if the coefficient of $x$ were positive?
2. What happens to the function if we change the constant term from 7 to -7?
3. How do you find the slope and y-intercept of a linear function like this one?
4. What is the value of $f(x)$ for $x = 2$?
5. How would you graph the function $f(x) = -4x + 7$?

Tip: For any linear function $f(x) = mx + b$, the slope is $m$ and the y-intercept is $b$.