Question

Write an equation for each translation of y=|x|. 9 units down

Answer 1

To translate a function downwards by 9 units you simply subtract 9 from the function, because the resulting y value is reduced by 9 so the graph of y is reduced, shifted downwards by 9.  So if:

y=|x|  then this shifted downwards by 9 units is:

y=|x|-9