Find g(x), where g(x) is the translation 9 units up of f(x)=x.


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.

Find g(x), where g(x) is the translation 9 units up of f(x) = x.

Learn how to translate the linear function f(x) = x by 9 units upwards to find g(x). This problem covers vertical translations in algebra and is ideal for students in Grades 7-9.

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