Pregunta
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Use transformations to explain how the graph of can be found by using the graph of .

Which of the following explains the transformations to find the graph of ?
Shifting of to the right 2 units and reflected about the -axis.
Shifting of to the left 2 units and reflected about the -axis.
Shifting of to the right 2 units and reflected about the -axis.
Shifting of to the left 2 units and reflected abo-it the -axis.

Ask by Lawson Wells. in the United States
Mar 20,2025

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To graph using , shift the graph right by 2 units and reflect it over the -axis.

Solución

To find the graph of using the graph of , we can analyze the transformations step by step.
  1. Starting Function: The base function is .
  2. Horizontal Shift: The expression indicates a horizontal shift. Specifically, means we shift the graph of to the right by 2 units. This is because we replace with , which moves the graph to the right.
  3. Reflection: The negative sign in front of the square root, , indicates a reflection about the -axis. This means that all the -values of the graph will be inverted (i.e., positive values become negative and vice versa).
Putting these transformations together, we can summarize the steps to obtain the graph of :
  • Start with the graph of .
  • Shift it to the right by 2 units.
  • Reflect the resulting graph about the -axis.
Thus, the correct explanation of the transformations to find the graph of is:
Shifting of to the right 2 units and reflected about the -axis.

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Mind Expander

To transform the graph of into the graph of , we first shift the graph of to the right by 2 units. This is because of the inside the square root, which moves our original function’s starting point from to . Next, the negative sign in front of the square root indicates a reflection over the -axis, flipping the graph upside down.
So, the correct explanation of the transformations is: shifting of to the right 2 units and reflected about the -axis! This transformation creates a function that starts at the point and goes downward from there.

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