Use the graph of

y equals f left parenthesis x right parenthesisy=f(x)

to graph the function

g left parenthesis x right parenthesis equals f left parenthesis x right parenthesis minus 2g(x)=f(x)−2.

y = f(x)

-6-4-2246-6-4-2246xy

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.

Use the graph of y = f(x) to graph the function g(x) = f(x) - 2.

Learn how to graph the transformation of y = f(x) by applying a vertical shift downward to get g(x) = f(x) - 2. This guide provides a step-by-step approach for students in Grades 9-10 to understand function transformations and graphing techniques.

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