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A coordinate plane's x-axis ranges from negative 12 to 12 and its y-axis ranges from negative 18 to 18, both by 2-unit increments. A curve of the function f left parenthesis x right parenthesis is plotted.

Interpret the key features of the graph to determine the transformation that occurred from its original function y=x−−√3
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(1 point)
Responses

This graph represents a shift down due to the change in the y-intercept from the parent function.
This graph represents a shift down due to the change in the y -intercept from the parent function.

This graph represents a shift to the left due to the change in the x-intercept from the parent function.
This graph represents a shift to the left due to the change in the x -intercept from the parent function.

This graph represents a shift up due to the change in the y-intercept from the parent function.
This graph represents a shift up due to the change in the y -intercept from the parent function.

This graph represents a shift to the right due to the change in the x-intercept from the parent function.
This graph represents a shift to the right due to the change in the x -intercept from the parent function.
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1 answer

To determine how the function \( f(x) \) transformed from the original function \( y = \sqrt{x} + 3 \), we need to analyze the changes represented in the graph that you described.

The function \( y = \sqrt{x} + 3 \) indicates that the parent function \( y = \sqrt{x} \) has been shifted upwards by 3 units due to the "+3" in the equation.

Therefore, if the graph you have represents the function \( f(x) \) as a transformation of \( y = \sqrt{x} + 3 \), it suggests that there has been some vertical shift (upwards or downwards), depending on the features of your specific graph.

Based on the responses provided:

  1. If the graph represents shifts vertically downwards, the closest statement is:

    • "This graph represents a shift down due to the change in the y-intercept from the parent function."

  2. If the graph is shifted vertically upwards, the corresponding statement would be:

    • "This graph represents a shift up due to the change in the y-intercept from the parent function."

If you analyze the graph and find it has shifted down, then the correct response would be the first statement. If it has shifted up from its original \( y = \sqrt{x} + 3 \), then the third statement would be appropriate.

Without the specifics of the graph in front of you, I'm unable to definitively state which transformation has occurred. You would select the option that best fits the observed behavior of the curve in the graph.