Question

The curve passes through the following marked points: left parenthesis negative 11 comma negative 2 right parenthesis, left parenthesis negative 4 comma negative 1 right parenthesis, left parenthesis negative 3 comma 0 right parenthesis, left parenthesis negative 2 comma 1 right parenthesis, and left parenthesis 5 comma 2 right parenthesis.

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

(1 point)

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 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.

Answer 1

This is a shift to the left due to the change in the x‑intercept from the parent function.

Reason: the parent y = ∛x has x‑intercept 0; the graph has x‑intercept (−3,0) and matches y = ∛(x+3) (e.g. ∛(−11+3)=∛(−8)=−2, ∛(5+3)=∛8=2), so it is shifted left 3 units.