If the domain of a function y=g(x) is D=[-2,6] and the range is R=[-8,10], find the domain and range of the function y=I g(2x) I +1.

the domain of g(2x) is 1/2 the domain of g(x) = [-1,3]

The range of g(2x) is unchanged.
But you have |g(2x)|+1, so what do you think?

Remember from pre-cal when you did scaling and translating of functions?