To find the y-intercept of the function $g\left(\frac{1}{2}x\right)$, let's break it down step by step.

1. Understanding the y-intercept of $g(x)$:
   The given information is that the absolute value function $g(x)$ has a y-intercept at $(0, 5)$. This means: $g(0) = 5$

2. Considering $g\left(\frac{1}{2}x\right)$:
   The function $g\left(\frac{1}{2}x\right)$ is a horizontal stretch of the function $g(x)$ by a factor of 2. However, horizontal stretches do not affect the y-intercept because the y-intercept occurs when $x = 0$.

3. Finding the y-intercept of $g\left(\frac{1}{2}x\right)$:
   To find the y-intercept of $g\left(\frac{1}{2}x\right)$, substitute $x = 0$ into the function: $g\left(\frac{1}{2} \times 0\right) = g(0)$ Since we know $g(0) = 5$, the y-intercept of $g\left(\frac{1}{2}x\right)$ is also at $(0, 5)$.

Conclusion:

The y-intercept of $g\left(\frac{1}{2}x\right)$ is the same as the y-intercept of $g(x)$, which is $(0, 5)$.

Would you like more details or have any questions? Here are some related questions you might find useful:

1. What happens to the graph of an absolute value function during a horizontal stretch or compression?
2. How does changing the coefficient of $x$ affect the symmetry of an absolute value function?
3. What are the effects of vertical and horizontal translations on the graph of $g(x)$?
4. How can we find the x-intercepts of the function $g\left(\frac{1}{2}x\right)$?
5. What are the transformations of the graph $g(x) = |x|$ for other modifications like $g\left(2x\right)$?

Tip: Horizontal transformations (stretches or compressions) only affect the x-values, while the y-values (like the y-intercept) stay unchanged unless there's a vertical transformation.