Questions: 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 $g(x)=f(4 x)$ ?

Solution

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.

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

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