Answer:
Beth is incorrect.
It is a translate to the right 5 units and up 1 unit.
When we solve x-5=0 we get x=5, not x=-5 which says we go right 5 units.
When we plug in 5 into the expression for g, we get 1 which means go up 1 as well.
Step-by-step explanation:
So [tex]g(x)=\sqrt{x-5}+1[/tex] is actually a translated 5 units and up 1 unit. Why?
Let's take there point (0,0) and figure out what the new point is on the translated graph.
We need to figure out when the inside of our square root for g is 0. This is where the graph of g will start at and continue on.
x-5=0 when x=5 ( I added 5 on both sides).
So let's plug in 5 to see what the new point is.
[tex]g(5)=\sqrt{5-5}+1[/tex]
[tex]g(5)=\sqrt{0}+1[/tex]
[tex]g(5)=0+1[/tex]
[tex]g(5)=1[/tex]
So the new graph, g, starts at the point (5,1).
