MHB Absolute Value Graph: Explaining |2-x| Horizontal Translation Right

AI Thread Summary
The discussion clarifies that the expression |2-x| can be rewritten as |x-2|, indicating a horizontal translation to the right. The key to understanding this shift lies in identifying the value of x that makes the expression inside the absolute value zero, which is x=2. This point corresponds to the vertex of the graph, which is shifted from the origin to the right by two units. While some participants express confusion about the implications of the transformation, using a table of values can help visualize the shift. Overall, the graph of |2-x| is confirmed to be a standard absolute value graph shifted two units to the right.
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Can someone explain to me why |2-x| would have a horizontal translation to the right? When I've always been taught that anytime you see a [+] it will translate to the left. The graph would be a regular |x| graph but it is shift 2 spots to the right. Thanks to anyone for help
 
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Ineedhelppp said:
Can someone explain to me why |2-x| would have a horizontal translation to the right? When I've always been taught that anytime you see a [+] it will translate to the left. The graph would be a regular |x| graph but it is shift 2 spots to the right. Thanks to anyone for help

There are several ways of thinking about this. One way: $|2-x|=|x-2|$, so you can see that it must be shifted to the right. In addition, one way of thinking about shifting is to ask yourself at what value of $x$ will the stuff inside the magnitudes be zero? That value of $x$ is going to have the corner that $|x|$ normally does at the origin. The nice thing about this second way of thinking is that it works for positive or negative shifts. Does this answer your question?
 
I think the second way I understand better, it still leaves me hazey because if |x-2|=|2-x| would mean no shift is taking place. And the only way at my level to show it is to the right, is a table of values with f(0),f(1) and f(2). Either way thanks for the further inlightenment.
 
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