To determine which graph represents the function \( y = f(x - 3) \) as a translation of the function \( y = f(x) \) by 3 units to the right, we need to identify a graph where the solid line (translated graph) is shifted to the right compared to the dotted line (original function).
In general, when a function \( f(x) \) is translated in the form of \( f(x - c) \), it shifts the graph to the right by \( c \) units. In this case, since \( c = 3 \), the graph should move to the right by 3 units.
To recap:
- If the original function's graph is at a certain x-coordinate, the translated graph will be at that x-coordinate plus 3.
- So, for a point on the original graph at \( (a, f(a)) \), the corresponding point on the translated graph will be at \( (a + 3, f(a)) \).
Look for a graph where the solid line is indeed the dotted line shifted 3 units to the right. If any of the graphs show this characteristic, that will be the correct answer.
Without viewing the actual graphs, I can't provide a specific choice, but check for the following:
- Identify the specific key points on the original function's graph (like intercepts or peaks).
- See if the corresponding points on the solid line are located 3 units to the right of those positions from the dotted line.
Select the graph that displays this behavior.