Question

Graph the following function using transformations. Be sure to graph all of the stages on one graph. State the domain and range. y = -SQRT x - 6.
My instructor is saying that I have to do more than one graph. Can anybody help me I am lost!

Answer 1

I will assume you mean
y = -√(x-6) and NOT y = -(√x) - 6

start with y = √x
using the following points, sketch the graph.
(0,0), (1,1), (4,2), (9,3), (16,4) ...
(notice I pick numbers that work out nicely)
You will have a "swooping" curve in the first quadrant that rises slowly.

now sketch y = - √x by reflecting your graph in the x-axis, (just flip it downwards)

then move the second graph 6 units to the RIGHT
(move each point 6 units to the right)

domain: any value of x , x ≥ 6
range: any real value of y , y ≤ 0 (all below the x-axis)

To verify, enter
(x-6)^.5
in the "first graph" in
http://rechneronline.de/function-graphs/

change "Range x-axis from" 6 to 20