When you stretch a linear function of the form \( f(x) = mx + b \) vertically by a factor \( k \), where \( m \) is the slope and \( b \) is the y-intercept, the new function becomes \( f(x) = k(mx + b) \).
For the given function:
\[ f(x) = \frac{1}{2}x - 4 \]
The slope \( m = \frac{1}{2} \) and the y-intercept \( b = -4 \). When we stretch this function by a factor of \( k = 3 \):
\[ g(x) = 3\left(\frac{1}{2}x - 4\right) = \frac{3}{2}x - 12 \]
Now, we see that:
- The new slope is \( \frac{3}{2} \), which is different from the original slope \( \frac{1}{2} \).
- The new y-intercept is \( -12 \), which is different from the original y-intercept \( -4 \).
Since both the slope and the y-intercept change, the correct answer is:
Both the slope and the y-intercept.