To find $g(x)$, which is the translation of $f(x) = x$ by 9 units upwards, we need to add 9 to the function $f(x)$.

Translation Rule:

• Translating a function upward by $k$ units means adding $k$ to the function.

So, for $g(x)$: $g(x) = f(x) + 9$ Since $f(x) = x$, we substitute: $g(x) = x + 9$

Therefore, the function after translation is: $g(x) = x + 9$

Would you like more details or have any questions?

Here are 5 related questions to expand on this concept:

1. What is the effect of translating a function downward instead of upward?
2. How does horizontal translation affect the function $f(x) = x$?
3. What happens to the graph of $f(x) = x$ if it's reflected over the x-axis?
4. How would you translate $f(x) = x$ by 5 units to the left?
5. How does vertical stretching affect the graph of $f(x) = x$?

Tip: When translating a function vertically, you only modify the output by adding or subtracting a constant from the entire function.