Analyze the transformation of \( g(x)=(x+3)^{2}-1 \) from \( f(x)=x^{2} \). What type of transformation occurs as a result of +3 inside of parenthesis? O Horizontal Shift 3 units Left Vertical Shift 3 units Down Vorizal Shift 3 units Up

The transformation \( g(x) = (x+3)^{2} - 1 \) from \( f(x) = x^{2} \) involves a horizontal shift caused by the "+3" in the parentheses. This means that every point on the graph of the original function \( f(x) = x^{2} \) will move 3 units to the left. So if you had a point like (0,0) on \( f \), it would now be at (-3,0) on \( g \). After the horizontal shift, there is also a vertical adjustment due to the "-1" outside the parentheses. This indicates that the entire graph is then shifted down by 1 unit. So not only has the graph moved left, but it has also dipped down, transforming the vertex from (0,0) to (-3,-1) in the new function \( g(x) \).