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

The function \( g(x) = (x + 3)^{2} - 1 \) involves two transformations from the parent function \( f(x) = x^{2} \). The term \( (x + 3) \) indicates a horizontal shift of the graph 3 units to the left. This occurs because we replace \( x \) with \( x + 3 \) in the function, which means every point on the graph moves leftward. On the other hand, the "-1" at the end of the transformation indicates a vertical shift. Specifically, this means that the entire graph is shifted down by 1 unit. So, all points, including the vertex, drop a unit lower. Sorting through the options, the correct transformation associated with the "-1" outside the parenthesis is a vertical shift 1 unit down.