Answer:
g(x)=x+2
Explanation:
So pretend the parent function was y=x.
Pretend we take this parent function and it move it right h units and up k units, then the equation becomes y=(x-h)+k. The assumption here was if h and k were positive.
Now if h is negative then it was moved left h units and if k was negative it was moved down k units.
So we have f(x)=x+6 and we want to move this 4 units right.
This effects the x since we are moving it left or right.
So I'm going to write g(x)=(x-4)+6.
We can simplify this:
g(x)=(x-4)+6
g(x)=x-4 +6
g(x)=x+2
Let's see if this actually moved us right 4 units.
Let's pick a point on f(x)=x+6 by choosing and x to plug in:
I choose x=0.
f(0)=0+6=6.
So the point (0,6) is on this line.
If I moved this points right 4 units it becomes (0+4,6)=(4,6).
This should be on our graph for the function above we found if we did it correctly.
Let's check it:
g(4)=4+2
g(4)=6
Guess what? (4,6) is a point on g because g(4)=6.
Let's do another.
Let's choose x=5.
f(5)=5+6=11 means we have the point (5,11) on the graph of f.
If we moved this point 4 units right it becomes (5+4,11)=(9,11).
Let's check to see if this is on g.
g(x)=x+2
g(9)=9+2
g(9)=11 so (9,11) is on g.