To find the function $g(x)$, where $g(x)$ is the translation of $f(x) = x^2$ by 1 unit down, you need to shift the function vertically down by 1 unit.

The general rule for a vertical translation of a function is:

• If you shift a function down by $c$ units, you subtract $c$ from the function.

Given $f(x) = x^2$, translating it down by 1 unit means: $g(x) = f(x) - 1 = x^2 - 1$

So, the translated function is: $g(x) = x^2 - 1$

---

Would you like a detailed explanation of how translations work, or have any other questions about this topic?

Here are 5 related questions you might find interesting:

1. What happens if we translate $f(x) = x^2$ 2 units up instead of down?
2. How would the graph of $g(x) = x^2 - 1$ look compared to the graph of $f(x) = x^2$?
3. What if we instead horizontally translated $f(x) = x^2$ by 3 units to the right?
4. How do you translate a function both horizontally and vertically?
5. What is the general form for vertical translation of any function?

Tip: Always remember that vertical translations affect the $y$-values directly by adding or subtracting a constant, while horizontal translations affect the $x$-values by shifting the input values.