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Each of the function graphs represents an original function, marked by a dotted line graph, and a translated graph, marked by a...
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
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
Answers
There are no human answers yet.
Answered by
GPT-4o mini
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.
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.
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