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

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We start with the original function:

$$
f(x)=x^{2}
$$

The given transformed function is:

$$
g(x)=(x+3)^{2}-1
$$

We can see two transformations:

1. The expression $$(x+3)^{2}$$ represents a horizontal shift. Since the expression is $$x+3$$, this corresponds to a shift **3 units to the left**.

2. The term $$-1$$ outside the parentheses affects the function after the squaring. This represents a vertical shift. Since $$-1$$ is subtracted, the graph of the function is shifted **1 unit down**.

The question specifically asks about the transformation as a result of the $$-1$$ outside of the parentheses. This corresponds to a **Vertical Shift 1 unit Down**.

Thus, the correct answer is:

Vertical Shift 1 unit Down.
The function $$ g(x) = (x+3)^2 - 1 $$ is a transformation of $$ f(x) = x^2 $$. The $$-1$$ outside the parentheses causes a **Vertical Shift 1 unit Down**.

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

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