Function f (z) represents the linear parent function. The graph of function f (a) is transformed to form function g (z) such that g (x) = f(x + 4) + 6.

The graph of function fe) is translated units and units v to create the graph of function 

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.

Function f (z) represents the linear parent function. The graph of function f (a) is transformed to form function g (z) such that g (x) = f(x + 4) + 6. The graph of function fe) is translated units and units v to create the graph of function.

Explore the transformation of the linear parent function f(x) to g(x) = f(x + 4) + 6. Learn about horizontal and vertical translations in function graphs, including shifting the graph 4 units to the left and 6 units up. Perfect for students in Grades 9-12 studying algebra and function transformations.

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