Describe how to transform the graph of f into the graph of g.
f left parenthesis x right parenthesis equals StartRoot x minus 8 EndRoot
 
and g left parenthesis x right parenthesis equals StartRoot x plus 4 EndRoot

To describe how to transform the graph of \( f(x) = \sqrt{x - 8} \) into the graph of \( g(x) = \sqrt{x + 4} \), we need to understand how the transformation affects the input \( x \).

### Step-by-Step Analysis:

1. **Starting with the basic function**:
   The function \( f(x) = \sqrt{x - 8} \) is a square root function shifted horizontally.

2. **Horizontal Shifts**:
   - For \( f(x) = \sqrt{x - 8} \), the graph of \( \sqrt{x} \) is shifted 8 units to the right because the expression inside the square root is \( x - 8 \).
   - For \( g(x) = \sqrt{x + 4} \), the graph of \( \sqrt{x} \) is shifted 4 units to the **left** because of the \( x + 4 \) inside the square root.

3. **Transformation Description**:
   To go from the graph of \( f(x) = \sqrt{x - 8} \) to \( g(x) = \sqrt{x + 4} \), you must shift the graph **12 units to the left**. This is because you are moving from \( x - 8 \) to \( x + 4 \), a total shift of \( 8 + 4 = 12 \) units left.

### Summary:
- The transformation from \( f(x) = \sqrt{x - 8} \) to \( g(x) = \sqrt{x + 4} \) is a **horizontal shift of 12 units to the left**.

Do you need any further details or clarifications?

Here are 5 related questions you might explore:
1. How would the transformation change if we had \( g(x) = \sqrt{x - 4} \)?
2. What happens if we add a vertical shift, such as \( g(x) = \sqrt{x + 4} + 2 \)?
3. How does the graph of \( f(x) = \sqrt{x} \) compare to \( g(x) = \sqrt{x + 4} \)?
4. How would the transformation change if we considered vertical stretches or compressions?
5. How would you describe the domain of both \( f(x) \) and \( g(x) \)?

**Tip**: Always remember that changes inside the function (like \( x + 4 \)) affect the graph horizontally, while changes outside (like \( \sqrt{x} + 2 \)) affect it vertically.

Describe how to transform the graph of f into the graph of g. f(x) = √(x - 8) and g(x) = √(x + 4)

Understand how to transform the graph of f(x) = √(x - 8) into g(x) = √(x + 4) through horizontal shifts. This detailed guide explains the steps needed to shift the graph 12 units to the left. Suitable for high school students, grades 9-11.

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