Questions: (b) The graph of y=g(x) is shown. Draw the graph of y=g(2x).
Transcript text: (b) The graph of $y=g(x)$ is shown. Draw the graph of $y=g(2 x)$.
Solution
Solution Steps
Step 1: Identify the key points of the original graph
The original graph \(y = g(x)\) has vertices at \((-4, 2)\), \((-2, -2)\) and \((0, 0)\).
Step 2: Apply the transformation
The transformation \(y = g(2x)\) is a horizontal compression by a factor of \(\frac{1}{2}\). This means the x-coordinates of the original graph are multiplied by \(\frac{1}{2}\), while the y-coordinates remain the same.