Questions: Graph the given functions, (f) and (g), in the same rectangular coordinate system. Describe how the graph of (g) is related to the graph of (f). (f(x)=-3 quad g(x)=3)

Graph the given functions, (f) and (g), in the same rectangular coordinate system. Describe how the graph of (g) is related to the graph of (f). (f(x)=-3 quad g(x)=3)
Transcript text: Graph the given functions, $f$ and $g$, in the same rectangular coordinate system. Describe how the graph of $g$ is related to the graph of $f$. \[ f(x)=-3 \quad g(x)=3 \]
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Solution

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Solution Steps

Step 1: Identify the Functions

The given functions are: f(x)=−3 f(x) = -3 g(x)=3 g(x) = 3

Step 2: Describe the Graphs

Both functions are horizontal lines. The graph of f(x)=−3 f(x) = -3 is a horizontal line at y=−3 y = -3 , and the graph of g(x)=3 g(x) = 3 is a horizontal line at y=3 y = 3 .

Step 3: Describe the Relationship

The graph of g(x)=3 g(x) = 3 is a vertical translation of the graph of f(x)=−3 f(x) = -3 by 6 units upwards.

Final Answer

The graph of g(x)=3 g(x) = 3 is a horizontal line 6 units above the graph of f(x)=−3 f(x) = -3 .

{"axisType": 3, "coordSystem": {"xmin": -10, "xmax": 10, "ymin": -5, "ymax": 5}, "commands": ["y = -3", "y = 3"], "latex_expressions": ["f(x)=−3f(x) = -3", "g(x)=3g(x) = 3"]}

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