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.