Shifting Graphs: Finding Corresponding Points

[Taryn1]

I feel like this should be a super easy problem, but I'm not understanding something about it.

The graph of y = f(x) passes through the points (0, 1), (1, 2), and (2, 3). Find the corresponding points on he graph y = f(x + 2) - 1. I graphed the (x + 2) - 1, but what does it mean by 'corresponding points'? The three points I named earlier lie on the line, but that's not the right answer (I have the answers in the back of the book). I just don't know how to get there correctly...

Here's the graph I got:

View attachment 4694

 

[Euge]

Hi Taryn,

The graph of $y = f(x + 2) - 1$ (or $y + 1 = f(x + 2)$) is obtained from the graph of $y = f(x)$ by shifting $2$ units to the left and $1$ unit down. So if I'm understanding the problem correctly, the point $(0,1)$ that lies on $y = f(x)$ corresponds to the point $(0 - 2, 1 - 1) = (-2,0)$ on the graph of $y = f(x + 2) - 1$. Similarly the point $(1,2)$ corresponds to $(1 - 2, 2 - 1) = (-1,1)$. If you display the answers here then I'll be sure exactly what correspondence they mean.

 

[Taryn1]

Thanks! That makes sense now. That's exactly the answers the book had. :)