Question

If y=x+2 were changed to y=x-1 how would tye graph of the new function compare with the first one

Answer 1

It would be shifted left.

Explanation:

Let's call the two functions
`f(x)=x+2` and
`g(x)=x-1.` If you want a tranformation that maps f into g, you can see that you simply have to subtract 3 from f: in fact,

`f(x)-2=(x+2)-3=x+2-3=x-1=g(x)`

Now, every transformation like
`f(x) { \to } f(x)+k.` results in a vertical translation, upwards if
`k>0` and downwards if
`k<0`. Since in our case
`k=-3,` the function is translated three units down.