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This question involves translating the graphs of two functions.

### Part (a): Translation of \( y = f(x) \)
The instruction says to translate the graph of \( y = f(x) \) to obtain the graph of \( y = f(x - 5) \). This is a **horizontal translation**.

- **Translation Rule**: For \( y = f(x - 5) \), the graph of \( f(x) \) is shifted 5 units **to the right**.

### Part (b): Translation of \( y = g(x) \)
The instruction says to translate the graph of \( y = g(x) \) to obtain the graph of \( y = g(x) - 2 \). This is a **vertical translation**.

- **Translation Rule**: For \( y = g(x) - 2 \), the graph of \( g(x) \) is shifted 2 units **downward**.

### Steps:
- In Part (a), move the entire graph 5 units to the right.
- In Part (b), move the entire graph 2 units down.

Would you like further details on these steps or clarifications?

Here are some related questions to extend the concepts:
1. How do horizontal and vertical translations affect the equations of functions?
2. What is the difference between translating by \( x \) units to the right and \( x \) units to the left?
3. Can translations change the shape of the graph, or only its position?
4. How would you translate \( f(x) \) vertically by 3 units up instead of 2 units down?
5. How does translating affect the domain and range of a function?

**Tip**: Always remember, shifting left or right modifies the \( x \)-value inside the function, while shifting up or down affects the entire function result.

The graph of y=f(x) is shown. Translate it to get the graph of y=f(x-5). The graph of y=g(x) is shown. Translate it to get the graph of y=g(x)-2.

Learn how to translate the graph of a function with both horizontal and vertical shifts. This problem involves translating y = f(x) to y = f(x - 5) and y = g(x) to y = g(x) - 2, demonstrating key concepts in graph transformations. Suitable for students in Grades 9-10.

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