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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
.

(1 point)
Responses

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

1 answer

To analyze the transformation of the function \(y = \sqrt{x} + 3\) from its parent function \(y = \sqrt{x}\), we first need to understand the original function and how the transformation affects its graph.

  1. Parent Function: The parent function \(y = \sqrt{x}\) has its graph starting at the origin (0,0) and increases to the right.

  2. Transformed Function: The function \(y = \sqrt{x} + 3\) indicates a vertical shift because of the "+ 3" added to the parent function. This moves every point on the graph of the parent function 3 units upwards.

Key Features of the Transformation:

  • The entire graph of \(y = \sqrt{x}\) is shifted upwards by 3 units.
  • There is no horizontal shift or change in the x-intercept since we are only adding a constant to the original function.

Based on this understanding, the correct response regarding the transformation that occurred from the original function \(y = \sqrt{x}\) to \(y = \sqrt{x} + 3\) is:

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