# Thread: Finding corresponding points for a translated graph

1. ## Finding corresponding points for a translated graph

Hi,

I'm quite lost with what my professor wants when he asks for "corresponding points" for a translated graph. I understand graph translations, but don't know where he's getting these points from.

For example, consider this problem:

The graph of f(x) = abs(x) is shifted to the right 3 units, then vertically stretched by a factor of 4, then reflected about the y axis, and finally shifted down 5 units. Write the final translated function h(x) and give it's graph. Label the corresponding three points.
The answer for this problem is h(x)=4*abs(-x-3)-5 and the three points are (-4,-1), (-2,-1), and (-3,-5).

I know that (-3,-5) is the vertex of the graph, so that is one of the points - but where is (-4,-1) and (-2,-1) coming from? Why not use X-intercepts instead? Help!

2. ## Re: Finding corresponding points for a translated graph

I don't think there is any deep answer to this. I suspect he just chose points that were 1 unit left and right of the vertex.

3. ## Re: Finding corresponding points for a translated graph

"Corresponding three points"? Three points corresponding to what? If the problem asks for the "corresponding three points" after the transformations then you must been given three points to apply the transformations to.