how to translate the graph y = |x| to obtain the graph of y = |x - 1| - 1?

Question

anonymous · Answer

$$y=|x-1|$$ moves $y=|x|$ to the RIGHT one unit

anonymous · Answer

the $-1$ out at the end moves it down one

michele_laino · Answer

Your equation can be rewritten as below:
$$y+1=|x-1|$$
so if we introduce the new coordinates X, Y defined as:
X=x-1,
and Y=y+1
your equation can be rewritten as below:
$$Y=|X|$$
which is in the desired form, so the equation of translation are:(1)
$$X=x-1, Y=y+1$$
now if in ewuations (1) we set X=0 and Y=0, namely the origin of the new system of coordinates, we get:
$$x=1,y=-1$$
namely you have to translate your coordinate system such that the new position of origin is located at point (1,-1)

anonymous · Answer

Thanks

michele_laino · Answer

thanks!

anonymous · Answer

Which of the following describes how to translate the graph y = |x| to obtain the graph of y = |x + 7|?

michele_laino · Answer

please, you have to perform the subsequent translation:
$$Y=y,X=x+7$$
where X,Y are the new axes, in the new coordinate system your equation can be rewritten as below:
$$Y=|X|$$
so like before, your new origin is located at the point (-7,0)

anonymous · Answer

so would it be 7 units up or down or left or right?