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

[buttretler]

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

 

[Ackbach]

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?

 

[buttretler]

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.