Question

Each of the function graphs represents an original function, marked by a dotted line graph, and a translated graph, marked by a solid line graph. Which graph shows that y=f(x−3) is the result of the function y=f(x) being translated by 3 units?(1 point)
Responses

Two lines drawn on coordinate plane. Both axes range from negative 5 to 5 in unit increment.
Image with alt text: Two lines drawn on coordinate plane. Both axes range from negative 5 to 5 in unit increment.

Two curves drawn on coordinate plane. Both axes range from negative 5 to 5 in unit increment.
Image with alt text: Two curves drawn on coordinate plane. Both axes range from negative 5 to 5 in unit increment.

Two parabolas drawn on coordinate plane. X-axis range from negative 9 to 4 and y-axis range from negative 1 to 9 in unit increment.
Image with alt text: Two parabolas drawn on coordinate plane. X-axis range from negative 9 to 4 and y-axis range from negative 1 to 9 in unit increment.

Two lines drawn on coordinate plane. X-axis range from negative 3 to 9 and y-axis range from negative 3 to 3 in unit increment.
Image with alt text: Two lines drawn on coordinate plane. X-axis range from negative 3 to 9 and y-axis range from negative 3 to 3 in unit increment.
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Answer 1

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.