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.

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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