The problem displayed asks to evaluate $f(-4.2)$ where $f(x) = \lfloor x \rfloor$, the floor function. The floor function $\lfloor x \rfloor$ outputs the greatest integer less than or equal to $x$.

Step-by-step solution:

1. Interpret $f(-4.2) = \lfloor -4.2 \rfloor$:

   • The floor of $-4.2$ is the greatest integer less than or equal to $-4.2$.
   • The greatest integer less than $-4.2$ is $-5$.

2. Final result: $f(-4.2) = -5$

Thus, the correct answer is $-5$.

Do you need more explanation or have further questions? Here are 5 related questions to explore:

1. What is the difference between the floor and ceiling functions?
2. How does the floor function behave with positive and negative decimal numbers?
3. Can you define the floor and ceiling functions formally?
4. How is the floor function used in real-life applications?
5. What is the floor of $-3.8$?

Tip: When using the floor function with negative numbers, remember that it "steps down" to the next integer, which might not be intuitive!