describe the translation from the parent graph

Question

the basic parent is y=x

for an absolute value it is y=|x|

describe the translation from the parent graph 

to y=x-4

Answer 1

The parent graph is y=x.  That is a line which goes from lower left to upper right with a slope of 1 (and at 45º).

 

The line with formula y=x-4, or y=(x-4), has (x-4) in place of x in the parent formula.  That means that for each original x, the formula will use a value that is 4 less.  This shifts any graph 4 units to the right (horizontally).

 

You also could say that the new formula (y+4)=x shifts any graph 4 units down (vertically).