We are given the point $(2, 4)$ on the graph of $y = f(x)$, and we need to find the corresponding coordinates of this point on the transformed graph of the function:

$f(x) = \frac{1}{2}(2x) - 1$

To proceed:

1. Substitute $x = 2$ into the equation of the new function:

$f(2) = \frac{1}{2}(2 \cdot 2) - 1$

Simplify the expression:

$f(2) = \frac{1}{2}(4) - 1 = 2 - 1 = 1$

Therefore, the corresponding coordinates of this point on the new graph are $(2, 1)$.

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Would you like more details or have any questions? Here are 5 related questions to expand on this:

1. How do transformations of functions affect their graphs?
2. What are the different types of function transformations (e.g., translations, stretches, reflections)?
3. How would the graph change if the function were $f(x) = \frac{1}{2}(2x + 1) - 1$?
4. What is the effect of multiplying the variable $x$ by a constant inside a function?
5. How do you calculate the inverse of a linear function?

Tip: When transforming functions, always look for changes in scaling, shifts, or reflections, as these will help you understand how the graph is modified.