Questions: Watch the video and then solve the problem given below. Click here to watch the video. Describe how the graph of g(x)=x-4 can be obtained from one of the basic graphs. Then graph the function. Select the correct choice below and fill in the answer box to complete your choice. A. Start with the graph of y= Shift it up 4 units. B. Start with the graph of y= Shift it down 4 units. C. Start with the graph of y= Shrink it horizontally by a factor of 4 . D. Start with the graph of y= Shift it left 4 units.

Watch the video and then solve the problem given below. Click here to watch the video. Describe how the graph of g(x)=x-4 can be obtained from one of the basic graphs. Then graph the function. Select the correct choice below and fill in the answer box to complete your choice. A. Start with the graph of y= Shift it up 4 units. B. Start with the graph of y= Shift it down 4 units. C. Start with the graph of y= Shrink it horizontally by a factor of 4 . D. Start with the graph of y= Shift it left 4 units.
Transcript text: Watch the video and then solve the problem given below. Click here to watch the video. Describe how the graph of $g(x)=x-4$ can be obtained from one of the basic graphs. Then graph the function. Select the correct choice below and fill in the answer box to complete your choice. A. Start with the graph of $y=$ $\square$ Shift it up 4 units. B. Start with the graph of $y=$ $\square$ Shift it down 4 units. C. Start with the graph of $y=$ $\square$ Shrink it horizontally by a factor of 4 . D. Start with the graph of $y=$ $\square$ Shift it left 4 units.
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Solution

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Solution Steps

Step 1: Start with the Basic Linear Function

The basic linear function is given by $y = x$. This graph is a straight line that passes through the origin (0,0) with a slope of 1.

Step 2: Determine the Direction and Magnitude of the Vertical Shift

Since $k = -4$, the graph is shifted downwards by 4 units.

Step 3: Apply the Vertical Shift

The resulting graph represents the function $g(x) = x - 4$, which is obtained by applying a vertical shift to the graph of $y = x$.

Final Answer:

The graph of the function $g(x) = x - 4$ is the graph of $y = x$ shifted downwards by 4 units.

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