Question

the graph of f(x) is shown. which graph represents g(x) = f(2x)?

Explanation:

Step1: Recall Horizontal Stretch/Compression Rule

For a function \( g(x) = f(kx) \), if \( |k| > 1 \), the graph of \( f(x) \) is horizontally compressed by a factor of \( \frac{1}{k} \). Here, \( k = 2 \), so the graph of \( f(x) \) will be compressed horizontally by \( \frac{1}{2} \).

Step2: Analyze Original Graph's Key Points

The original graph \( f(x) \) has its "wavy" part near the origin. When we compress horizontally by \( \frac{1}{2} \), the x - coordinates of all points on \( f(x) \) are multiplied by \( \frac{1}{2} \), making the graph narrower.

Step3: Compare with Options

• The first option (left - most) shows a graph that is narrower (compressed horizontally), which matches the horizontal compression by a factor of \( \frac{1}{2} \) for \( g(x)=f(2x) \). The other options either have the wrong width (too wide or not compressed enough) or incorrect shape positioning.

Answer:

The Left - most Graph (the first graph among the four options)