Write an equation for then translation of y = IXI

what kind of translation?

To shift the graph up k and right h, you need

y-k = f(x-h)

So, to shift f(x) = |x| up 2 and right 3, you have

y-2 = |x-3|
or,
y = |x-3|+2

h and k may be negative, for shifting down and left.

2 units down sorry

Y= |x+2|

To write an equation for the translation of the function y = |x|, we need to determine the direction and distance of the translation. Assuming you're referring to a horizontal translation (shifting left or right), the equation will be of the form y = |x - h|, where "h" represents the horizontal shift.

If the function y = |x| is translated to the right by "a" units, the equation becomes y = |x - a|. On the other hand, if the function is translated to the left by "a" units, the equation becomes y = |x + a|.

So, to write an equation for the translation of y = |x|, we need to know the direction and distance of the translation.