Questions: The graph above is of g(x) obtained from transforming f(x)=x^2. Find g(x).

The graph above is of g(x) obtained from transforming f(x)=x^2. Find g(x).
Transcript text: The graph above is of $g(x)$ obtained from transforming $f(x)=x^{2}$. Find $g(x)$.
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Solution

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Solution Steps

Step 1: Identify the Parent Function

The parent function given is \( f(x) = x^2 \).

Step 2: Analyze the Transformation

Observe the graph of \( g(x) \). The graph appears to be a vertical shift of the parent function \( f(x) = x^2 \). The vertex of the parabola is at (0, 4) instead of (0, 0).

Step 3: Determine the Transformation

Since the vertex has moved up by 4 units, the transformation applied to \( f(x) = x^2 \) is a vertical shift upward by 4 units.

Final Answer

The function \( g(x) \) is given by: \[ g(x) = x^2 + 4 \]

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