Questions: Translate each graph as specified below. (a) The graph of y=f(x) is shown. Translate it to get the graph of y=f(x-3). (b) The graph of y=g(x) is shown. Translate it to get the graph of y=g(x)+5.

Translate each graph as specified below. (a) The graph of y=f(x) is shown. Translate it to get the graph of y=f(x-3). (b) The graph of y=g(x) is shown. Translate it to get the graph of y=g(x)+5.
Transcript text: Translate each graph as specified below. (a) The graph of $y=f(x)$ is shown. Translate it to get the graph of $y=f(x-3)$. (b) The graph of $y=g(x)$ is shown. Translate it to get the graph of $y=g(x)+5$.
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Solution

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Solution Steps

Step 1: Understanding the Problem

The problem requires translating the given graphs of functions as specified. We need to translate the graph of \( y = f(x) \) to get \( y = f(x - 3) \) and the graph of \( y = g(x) \) to get \( y = g(x) + 5 \).

Step 2: Translating \( y = f(x) \) to \( y = f(x - 3) \)

To translate the graph of \( y = f(x) \) to \( y = f(x - 3) \), we need to shift the graph horizontally to the right by 3 units. This is because the transformation \( f(x - 3) \) indicates a shift to the right.

Step 3: Translating \( y = g(x) \) to \( y = g(x) + 5 \)

To translate the graph of \( y = g(x) \) to \( y = g(x) + 5 \), we need to shift the graph vertically upwards by 5 units. This is because the transformation \( g(x) + 5 \) indicates a shift upwards.

Final Answer

  • For part (a), shift the graph of \( y = f(x) \) to the right by 3 units to get \( y = f(x - 3) \).
  • For part (b), shift the graph of \( y = g(x) \) upwards by 5 units to get \( y = g(x) + 5 \).
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