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To graph \( g(x) = f(x) + 4 \) based on the provided graph of \( f(x) \), you need to apply a **vertical shift** to the function \( f(x) \). Here's the step-by-step process:

1. **Understand the transformation**: The function \( g(x) = f(x) + 4 \) represents a vertical shift of \( f(x) \) by 4 units **upward**. Every point on the graph of \( f(x) \) will move up by 4 units.

2. **Apply the transformation**:
   - Take the \( y \)-coordinates of all key points on the graph of \( f(x) \).
   - Add 4 to each \( y \)-coordinate while keeping the \( x \)-coordinates the same.

For example:
   - If there is a point at \( (x_1, y_1) \) on \( f(x) \), the corresponding point on \( g(x) \) will be \( (x_1, y_1 + 4) \).

3. **Example** from the graph:
   - At \( x = -6 \), the point on \( f(x) \) is \( (-6, 0) \). So, on \( g(x) \), it will be \( (-6, 0 + 4) = (-6, 4) \).
   - At \( x = -4 \), the point on \( f(x) \) is \( (-4, 2) \). So, on \( g(x) \), it will be \( (-4, 6) \).
   - Continue this process for each of the points.

4. **Sketch the new graph**: After moving all the points by 4 units upward, plot the new points on the graph and connect them to form the graph of \( g(x) \).

Would you like further details on graph transformations or have any questions? 

Here are 5 related questions:
1. How does a vertical shift differ from a horizontal shift in graph transformations?
2. What happens when we subtract a value from \( f(x) \) (e.g., \( g(x) = f(x) - 3 \))?
3. How can we apply transformations like reflection or stretching to functions?
4. What are the effects of adding constants to \( x \) instead of to \( f(x) \)?
5. How would the graph look if we applied both a vertical shift and a horizontal shift?

**Tip**: When performing vertical shifts, always focus on the \( y \)-coordinates and adjust them directly by the amount of the shift.

Use the graph of y = f(x) to graph the function g(x) = f(x) + 4.

Learn how to graph g(x) = f(x) + 4 by applying a vertical shift to the function f(x). This detailed guide explains the transformation process and how to move points on the graph by 4 units upward. Suitable for students in Grades 8-10.

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