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?

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.