Algebra 2, absolute value written problem

Question

Katie was given this absolute value graph and needs to come up with the equation, domain, range and intercepts. The parent function is y = |x|...and from her knowledge with translations she knows that it has translated horizontally to the right 4 units. So she says the new equation must be y = |x+4|. The domain is all values of x. The range is all values of y greater than or equal to zero. The y-intercept is (0,4). There isn’t an x-intercept, because it just sits at (4,0). What is the correct equation for this graph and why?

Answer 1

IF you shift it to the right 4 units, the correct equation is y = the absolute value of (x-4)

You need a negative sign in front of the 4

when x=4, then y=4-4 = 0, that's the point (4,0) which is the shift to the right by 4 from (0,0) the origin.

She got the range of y and y intercept correct. But then they are the same whether you shifted the graph left or right.