Questions: Suppose f(x)=x^2. What is the graph of g(x)=f(4x)?

Suppose f(x)=x^2. What is the graph of g(x)=f(4x)?
Transcript text: Suppose $f(x)=x^{2}$. What is the graph of $g(x)=f(4 x)$ ?
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Solution

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Solution Steps

Step 1: Understanding the Function Transformation

The given function is \( f(x) = x^2 \). We need to determine the graph of \( g(x) = f(4x) \).

Step 2: Applying the Transformation

The transformation \( g(x) = f(4x) \) means we replace \( x \) with \( 4x \) in the function \( f(x) \). Therefore, \( g(x) = (4x)^2 = 16x^2 \).

Step 3: Analyzing the Effect of the Transformation

The function \( g(x) = 16x^2 \) is a vertical stretch of the original function \( f(x) = x^2 \) by a factor of 16. This makes the parabola narrower.

Final Answer

The correct graph is option D, which shows a narrower parabola compared to the original \( f(x) = x^2 \).

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