The given transformation of the linear parent function $f(x)$ to $g(x) = f(x + 4) + 6$ represents a translation of the graph. Let's break down the transformation:

1. Horizontal Translation: The term $f(x + 4)$ indicates a horizontal shift. Since it’s in the form $f(x + h)$, where $h = 4$, the graph is shifted 4 units to the left.

2. Vertical Translation: The $+6$ outside of the function represents a vertical shift. This translates the graph 6 units up.

Summary:

• The graph of $f(x)$ is translated 4 units left and 6 units up to form the graph of $g(x)$.

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Do you want more details or have any questions?

Here are 5 related questions:

1. How do we identify transformations in other functions, like quadratic or cubic?
2. What happens if the translation involves a negative number inside the function?
3. How would the transformation change if the equation was $g(x) = f(x - 4) + 6$?
4. How do horizontal and vertical stretches affect the graph of a function?
5. Can translations be combined with reflections or dilations for more complex transformations?

Tip: Always remember, horizontal shifts are opposite in direction to the sign inside the function.