To graph $g(x) = f(x) - 2$ using the graph of $y = f(x)$, follow these steps:

1. Understand the transformation: The expression $g(x) = f(x) - 2$ represents a vertical shift of the function $f(x)$ downward by 2 units. This means that every point on the graph of $y = f(x)$ will move down by 2 units to create the graph of $g(x)$.

2. Apply the shift: For each point $(x, y)$ on the graph of $y = f(x)$, find the corresponding point on $y = g(x)$ by subtracting 2 from the $y$-coordinate, resulting in the point $(x, y - 2)$.

3. Plot the points: Move each point on the original graph down by 2 units and plot the new points to form the graph of $g(x)$.

4. Draw the new graph: Connect the new points smoothly, keeping the same shape as the original graph of $f(x)$, but now shifted downward.

If you'd like, I can provide further details on this transformation or discuss more examples.

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Here are five related questions to deepen your understanding:

1. How would the graph change if $g(x) = f(x) + 2$ instead?
2. What transformation occurs if the function becomes $g(x) = f(x) \cdot 2$?
3. How does the graph change if we use $g(x) = -f(x)$ instead?
4. What happens if we apply a horizontal shift, such as $g(x) = f(x - 2)$?
5. How can transformations be combined, like $g(x) = f(x - 2) + 3$?

Tip: Vertical transformations directly affect the $y$-values by adding or subtracting, making it easier to visualize by moving the graph up or down without changing the shape.