Questions: (b) The graph of y=g(x) is shown. Draw the graph of y=g(2x).

(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 $y=g(2 x)$.
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Solution

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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.

Step 3: Calculate the transformed points
  • \((-4, 2)\) transforms to \((-4 \times \frac{1}{2}, 2) = (-2, 2)\)
  • \((-2, -2)\) transforms to \((-2 \times \frac{1}{2}, -2) = (-1, -2)\)
  • \((0, 0)\) transforms to \((0 \times \frac{1}{2}, 0) = (0, 0)\)
Step 4: Plot the transformed points and draw the graph

Plot the points \((-2, 2)\), \((-1, -2)\), and \((0, 0)\) on the coordinate plane. Connect these points to form the graph of \(y = g(2x)\).

Final Answer

The graph of \(y=g(2x)\) has vertices at \((-2, 2)\), \((-1, -2)\), and \((0, 0)\). It is a horizontally compressed version of the original graph.

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