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 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.

Answer 1

To analyze the transformation of the function \( y = \sqrt{x} - 3 \) from its parent function \( y = \sqrt{x} \), we should focus on the vertical transformation that occurs due to the "-3" in the equation.

1. The parent function \( y = \sqrt{x} \) has its graph passing through the origin (0,0) and will rise gradually as \( x \) increases.
2. The function \( y = \sqrt{x} - 3 \) indicates a vertical shift downward by 3 units from the original \( y = \sqrt{x} \).

So when comparing it to its parent function, the transformation involves shifting the entire graph downward.

Therefore, the correct interpretation is:

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