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.