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)

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. 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.

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 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 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.
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a b c or d

GPT-4o mini · Answer

To determine which graph shows that $ y = f(x-3) $ is the result of the function $ y = f(x) $ being translated by 3 units to the right, we need to understand how function translations work. When we have $ y = f(x - c) $, it translates the graph of $ f(x) $ to the right by $ c $ units. In this case, since $ c = 3 $, the graph of $ f(x) $ should shift 3 units to the right. Look for a graph where the solid graph (translated function) maintains the shape of the dotted graph (original function), but is shifted to the right by 3 units. Without the images to directly analyze, I can advise you to look for: - A graph where the "dotted" line (representing $ f(x) $) is clearly 3 units to the left of the "solid" line (representing $ f(x-3) $). Based on this understanding, choose the option that matches that description.