Question

why is that when you translate a graph horizontally to the right, you have to subtract a value??

Answer 1

Imagine you have the function \[f(x)=3x\]so f(5)=15 and the point (5,15) is on the graph.\[\]Now if you want to move that graph to the right by 3 units, we would need the point (8,15) to be on the graph. Our new input value, x=8 must give us an output of 15 when we use our function. So we subtract 3 from x before we apply it into the function. So our new function would be
\[g(x)=f(x-3)=3(x-3)=3x-9\]
\[g(8)=3(8)-9=24-9=15\]
as required.
\[\]
So we had to subtract 3 when we moved to the right because the input values for our new graph are now larger than they were for the original function.

Answer 2

lot of info.