SOLUTION: can someone please help me with this As soon as possible? Use transformations to sketch the function y=-3(2^x+6)-1. State the domain and range

I'll assume you meant  and not ,
which is what you wrote meant because you didn't put the 
exponent in parentheses and so the +6 didn't get included 
in the exponent when you don't put parentheses to include it.

Start with .  I'll mark the point (1,2)
and show what happens to that point:
Domain (-oo,oo), Range (0,oo)



Next replace x by x+6 which shifts the graph 6 units left.
This is the graph is of .
Notice that the point (1,2) shifts horizontally 6 units left 
to (-5,2): 
Domain (-oo,oo), Range (0,oo)


Next multiply by -1, which reflects it into (across) the x-axis
This is the graph of 
Notice that the point (-5,2) reflects across the x-axis to (-5,-2): 
Domain (-oo,oo), Range (-oo,0)


Next multiply by 3 which stretches it vertically by a factor of 3.  
This is as if the graph were on a rubber sheet and we stretched the 
rubber sheet three times vertically.
This is the graph of 
Notice that the point (-5,-2) stretches vertically by a factor of
3 to (-5,-6): 
Domain (-oo,oo), Range (-oo,0)


Finally we add -1 which shifts it down 1 unit.
Notice that the point (-5,-6) shifts vertically down to (-5,-7) 
This is the final graph:
Domain (-oo,oo), Range (-oo,-1).  Notice that the horizontal
asymptote did not move until now. It moved from the x-axis (y=0)
to the green dotted line y=-1:


Edwin