The problem asks to solve for the input when the output is $-3$, given the function $f(x) = \frac{1}{2}x - 3$.

We need to find the value of $x$ when $f(x) = -3$.

Steps:

1. Set the function equal to the output: $f(x) = -3$ $\frac{1}{2}x - 3 = -3$

2. Add 3 to both sides of the equation: $\frac{1}{2}x = 0$

3. Multiply both sides by 2 to solve for $x$: $x = 0$

So, the input is $x = 0$ when the output is $-3$.

Would you like a more detailed explanation or have any questions?

Here are some related questions:

1. How do you solve linear equations with fractions?
2. What is the general process for solving $f(x) = y$?
3. How do you graph the function $f(x) = \frac{1}{2}x - 3$?
4. What does the slope represent in the function $f(x) = \frac{1}{2}x - 3$?
5. How can you verify your solution for $x$ by substitution?

Tip: Always isolate the variable by reversing operations step by step to maintain balance in the equation.