Questions: Complete the following. (a) The graph of y=h(x) is shown. Draw the graph of y=2h(x-4).

Complete the following. (a) The graph of y=h(x) is shown. Draw the graph of y=2h(x-4).
Transcript text: Complete the following. (a) The graph of $y=h(x)$ is shown. Draw the graph of $y=2 h(x-4)$.
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Solution

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Solution Steps

Step 1: Horizontal Shift

The graph of $y = h(x-4)$ is obtained by shifting the graph of $y = h(x)$ four units to the right. The points $(-2, 4)$, $(0, 0)$, and $(4, 2)$ on the original graph become $(2, 4)$, $(4, 0)$, and $(8, 2)$ respectively.

Step 2: Vertical Stretch

The graph of $y = 2h(x-4)$ is obtained by vertically stretching the graph of $y = h(x-4)$ by a factor of 2. This means multiplying the y-coordinates of the shifted points by 2. Thus the points $(2, 4)$, $(4, 0)$, and $(8, 2)$ become $(2, 8)$, $(4, 0)$, and $(8, 4)$ respectively.

Final Answer:

The transformed graph will pass through the points $(2, 8)$, $(4, 0)$, and $(8, 4)$. It's a horizontal shift of 4 units to the right, followed by a vertical stretch by a factor of 2.

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