Mapping rule of Transformations & Domain and Range?

Question

What mappingrule describes the transformation of graph 1 onto graph 2?

Graph 1's points are: (0,0),(-1,1),(1,1),(-2,4)(2,4)
Graph 2's points are:(-6,3)(-8,3)(-7,-5)

(x,y) --> (x+5, -1/2y - 7)
(x,y) --> (x+5, -2y + 7)
(x,y) --> (x-7, -1/2y - 5)
(x,y) --> (x-7, -2y + 5)

How exactly would you figure it out? Any help?

Also: for domain and range of a function (not related to the above question), what is the easiest possible way to find the domain, range, or both, to a function? How would you write it? Thanks :)

Answer 1

The problem is that you don't have the same number of points in the first and second graph.

Normally, I would try each pair of points in the first graph with the second. For example, the first part of the transformation is either "new x = old x + 5" or "new x = old x - 7"
So, are there ANY three points in the first set that have this relationship with the second?
The answer is yes:
(0,0) to (-7,5)
(-1,1) to (-8, 3)
and (1,1) to (-6,3)

So we know that the answer is the third or fourth.
For these, does "-1/2y-5" or "-2y+5" fit them all?
for (0,0) to map to (-7,5) you need the "plus 5" instead of the "minus 5".
Does this -2y+5 fit the other two?
(-1,1) to (-8, 3): -2*1+5 DOES equal 3, so that works. Likewise, the next pair works as well!
So the answer is the last of the selections above:
(x,y) --> (x-7, -2y+5).