To analyze the transformed function \( f(x) = 4x + 5 - 2 \), we can simplify it first:
\[ f(x) = 4x + 3 \]
Now, we compare this with the parent function \( g(x) = 4x \).
The transformation from \( g(x) \) to \( f(x) \) involves a vertical translation, since both functions have the same slope (4), and therefore the same steepness.
The change in the function is given by the addition of 3 to \( 4x \). This means that the graph of the transformed function \( f(x) = 4x + 3 \) is:
- A vertical translation upward by 3 units compared to the parent function \( g(x) = 4x \).
None of the options directly match this result. Let's check the adjustments again for any possible miscalculations in answer choices focusing strictly on horizontal shifts (which aren't present) and vertical shifts.
Since there is no horizontal shift either left or right and we see a vertical shift (adding 3), if we were to find translations to match, we'd summarize as:
The answer is that the transformed function \( f(x) = 4x + 3 \) is obtained by moving the graph of \( g(x) = 4x \) up 3 units.
Given the options listed, they all represent combinations of left/right and down/up translations that do not align. Thus, no correct option is available among the choices provided that describes this transformation accurately.