MHB Shifting Graphs: Finding Corresponding Points

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The discussion centers on finding corresponding points between the graphs of y = f(x) and y = f(x + 2) - 1. The original graph passes through the points (0, 1), (1, 2), and (2, 3). By applying the transformations, the corresponding points are calculated as follows: (0, 1) shifts to (-2, 0), (1, 2) shifts to (-1, 1), and (2, 3) shifts to (0, 2). The participants confirm that these transformations align with the answers provided in the textbook. Understanding the shifts clarifies the problem and resolves the initial confusion.
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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
 

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