The function $f(x) = -2x + 3$ is a linear function. Since there are no restrictions on $x$ (such as square roots, logarithms, or denominators that could make the function undefined), the domain of this function includes all real numbers.

Thus, the domain of $f(x)$ is:

$\boxed{(-\infty, \infty)}$

Would you like further details on graphing linear functions or any related concepts?

Here are five related questions:

1. What is the range of the function $f(x) = -2x + 3$?
2. How does the slope of $f(x) = -2x + 3$ affect the graph's steepness?
3. What is the $y$-intercept of $f(x) = -2x + 3$?
4. How do you find the $x$-intercept of a linear function?
5. How does the graph of $f(x) = -2x + 3$ compare to $f(x) = 2x + 3$?

Tip: For linear functions of the form $f(x) = mx + b$, the domain is always all real numbers, unless restrictions are explicitly given.