Questions: Describe how the graph of the function g(x) = 1/2x - 6 can be obtained from the basic graph. Then graph the function. Start with the graph of h(x) = x. Then it vertically by a factor of . Finally, shift it unit(s). (Type an integer or a simplified fraction.)

$Describe how the graph of the function g(x) = 1/2x - 6 can be obtained from the basic graph. Then graph the function. Start with the graph of h(x) = x. Then it vertically by a factor of . Finally, shift it unit(s). (Type an integer or a simplified fraction.)$

Transcript text: Describe how the graph of the function $\mathrm{g}(\mathrm{x})=\frac{1}{2}|\mathrm{x}|-6$ can be obtained from the basic graph. Then graph the function. Start with the graph of $h(x)=|x|$. Then $\square$ it vertically by a factor of $\square$ . Finally, shift it $\square$ unit(s). (Type an integer or a simplified fraction.) Choose the correct graph below.

Solution

Solution Steps

Step 1: Identify the Basic Graph

The basic graph is $ h(x) = |x| $.

Step 2: Vertical Scaling

The function $ g(x) = \frac{1}{2}|x| - 6 $ involves a vertical scaling of the basic graph $ h(x) = |x| $ by a factor of $\frac{1}{2}$.

Step 3: Vertical Shifting

The function $ g(x) = \frac{1}{2}|x| - 6 $ involves shifting the graph vertically downward by 6 units.

Final Answer

Start with the graph of $ h(x) = |x| $. Then scale it vertically by a factor of $\frac{1}{2}$. Finally, shift it 6 unit(s) downward.

{"axisType": 3, "coordSystem": {"xmin": -10, "xmax": 10, "ymin": -10, "ymax": 10}, "commands": ["y = (1/2)*abs(x) - 6"], "latex_expressions": ["$y = \\frac{1}{2}|x| - 6$"]}

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