Question

Determine the domain and range of the function. Also describe translation to vertex. (picture)

Answer 1

Domain: all reals
If you need it in interval notation, its (-[infinity symbol], [infinity symbol])
If that last part confused you, ignore it because it means you just need to write all reals.
Pretty sure all of them have the same answer in this regard.

Range: y is greater than or equal to the last value in the equation.
For example: for 7 it would be y is greater than/equal to -6.

Translations:
4: shifted right 3
5: shifted down 7
6: shifted up 4
7:: left 1, down 6.

Any time you have an (x-n) n just being a letter I substituted for a number, the graph will be moved right n spaces from the origin. (x+n) moves it left.
If there are no parentheses, it means the graph is moved up or down, a minus indicating the graph being moved down by the number and a plus indicated it being moved up by the number.