Questions: Complete the following. (a) The graph of y=h(x) is shown. Draw the graph of y=2h(x)+1.

Complete the following. (a) The graph of y=h(x) is shown. Draw the graph of y=2h(x)+1.
Transcript text: Complete the following. (a) The graph of $y=h(x)$ is shown. Draw the graph of $y=2 h(x)+1$.
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Solution

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Solution Steps

Step 1: Identify the Transformation

The given function is \( y = h(x) \). We need to transform it to \( y = 2h(x) + 1 \).

Step 2: Apply the Transformation

The transformation involves two steps:

  1. Vertical Stretch: Multiply the function \( h(x) \) by 2, resulting in \( y = 2h(x) \).
  2. Vertical Shift: Add 1 to the result, giving the final transformation \( y = 2h(x) + 1 \).

Final Answer

The graph of \( y = 2h(x) + 1 \) is a vertically stretched and shifted version of \( y = h(x) \).

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