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.

Question

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 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.
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 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.

Answer 1

To determine the transformation that occurred from the original function \( y = \sqrt{x} \) to the function \( f(x) \), we need to analyze the given function.

1. Base Function: The base function is \( y = \sqrt{x} \). This function has its x-intercept at \( (0, 0) \) and is only defined for \( x \geq 0 \).

2. Altered Function: The function provided is \( y = \sqrt{x} - 3 \). This indicates that the function undergoes a vertical transformation.

Key Features:

• Vertical Shift: The "-3" in \( \sqrt{x} - 3 \) means that every point on the curve of the base function \( \sqrt{x} \) is shifted down by 3 units.

Therefore, the correct interpretation of the transformation from the parent function \( y = \sqrt{x} \) to the new function \( y = \sqrt{x} - 3 \) is that:

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