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 $y=g(x)+5$.

Solution

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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