Interpret the key features of the graph to determine the transformation that occurred from its original function y=3−−√x. the new function y=3--√x+3

Question

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(1 point)
Responses

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.

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 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 left due to the change in the x-intercept from the parent function.

Answer 1

To analyze the transformation from the original function \( y = \sqrt{3 - x} \) to the new function \( y = \sqrt{3 - x} + 3 \), let's break it down.

1. Original Function: \( y = \sqrt{3 - x} \)

   • This function is a square root function that opens downwards, with its maximum (at \( x = 3 \)) being 0.

2. New Function: \( y = \sqrt{3 - x} + 3 \)

   • The transformation to this new function adds 3 to the entire function.

Key Transformation:

• Vertical Shift:
  • Since we are adding 3 to the function, this results in a vertical shift upward by 3 units.

Conclusion:

The correct interpretation of the transformation is:

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