Question

If y = x + 2 were changed to y = x - 1, how would the graph of the new function compare with the first one? A. It would be shifted up. B. It would be shifted left. C. It would be shifted down. D. It would be less steep.

Answer 1

it would be less steep

Explanation:

Answer 2

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, so the answer is C.