On the graph, plot all relevant points for y=the absolute value of x-1. Then give the equation for a graph that shifts up 3 units and to the left 4 units. If it is a function, give its domain and range.

Question

Thank you!!

Answer 1

The original function is a "V" that rises from x=1,y=0 with a 45 degree angle to the right, and a -45 degree angle to the left. To shift it by the amounts described, the function becomes
y = 3 + |x + 3|. It is a V with the bottom at x = -3, y = 3.

Plot it yourself and you should see why, and what the range is.