+41 which represents the function f(x) = x+1 as a vertical translation one unit up using coordinate notation?
a. (x,y-1)
b. (x,y+1)
c.(x-1,y)
d.(x+1,y)
If you move the origin from (0,0) to the point (a,b) then the new x and y co-ordinates translate to
(x-a) (y-b)
here you are moving the origin to the point (0,1) so all points now translate to (x-0) (y-1)
or just x , (y-1)
So (a) is your answer.
In general,if you have a function y=f(x) then by moving the origin to the point (a,b) the new (translated or shifted) function becomes (y-b) = f(x-a).This is very useful to remember,and is commonly used to simplify some types of problems. (Like the equations of circles) You can check this with your original problem, you get the function shifting to (y-1) =f(x) which of course gives you the set of points
(x, {y-1} )
