Questions: Translating the graph of a function: one step 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)+5. b) The graph of y=g(x) is shown. Translate it to get the graph of y=g(x+3).

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

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Solution Steps

Step 1: Understanding the Problem

We need to translate the given graphs as specified:

  • Part (a): Translate the graph of \( y = f(x) \) to get \( y = f(x) + 5 \).
  • Part (b): Translate the graph of \( y = g(x) \) to get \( y = g(x + 3) \).
Step 2: Translation for Part (a)

To translate \( y = f(x) \) to \( y = f(x) + 5 \):

  • This is a vertical translation.
  • We move the entire graph up by 5 units.
Step 3: Translation for Part (b)

To translate \( y = g(x) \) to \( y = g(x + 3) \):

  • This is a horizontal translation.
  • We move the entire graph to the left by 3 units.

Final Answer

  • For Part (a), the graph of \( y = f(x) \) is translated up by 5 units.
  • For Part (b), the graph of \( y = g(x) \) is translated to the left by 3 units.
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