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Let's examine the function transformation step-by-step.

1. **Given functions:**
   - \( f(x) = x \)
   - \( g(x) = \frac{1}{2}f(x) - 4 \)

2. **Substitute \( f(x) \) into \( g(x) \):**
   Since \( f(x) = x \), we can rewrite \( g(x) \) as:
   \[
   g(x) = \frac{1}{2}x - 4
   \]

3. **Transformation Analysis:**
   - **Vertical Compression:** The coefficient \( \frac{1}{2} \) scales the function vertically, compressing it by a factor of \( \frac{1}{2} \).
   - **Vertical Shift:** The term \( -4 \) shifts the graph downward by 4 units.

4. **Answer Choices:**
   - The graph of \( g(x) \) is **a vertical compression of** the graph of \( f(x) \).
   - The y-intercept of \( g(x) \) is **4 units below** the graph of \( f(x) \).

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

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Here are five related questions for additional practice:
1. How would the transformation change if \( g(x) = 2f(x) - 4 \)?
2. What effect would adding \( +4 \) instead of \( -4 \) have on \( g(x) \)?
3. How does a horizontal compression differ from a vertical compression?
4. What is the y-intercept of \( g(x) = \frac{1}{2}x - 4 \)?
5. How would the function change if the transformation was \( g(x) = \frac{1}{2}f(x + 3) - 4 \)?

**Tip:** To find the y-intercept of a transformed function, substitute \( x = 0 \) into the equation.

The function f(x) = x is transformed to create g(x) = (1/2)f(x) - 4. The graph of g(x) is __ the graph of f(x) and the y-intercept of g(x) is __ the graph of f(x).

Explore the transformation of the function f(x) = x to g(x) = (1/2)f(x) - 4, involving vertical compression and vertical shift. Understand how the graph of g(x) changes in relation to f(x), including the impact on the y-intercept.

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