whats the difference between say...

or what translation does it make to the graph? It was on a test I wrote but I was never really taught it. Is it like a reciprocal multiplied by 5?

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- February 24th 2009, 10:03 AMbrentwoodbc[SOLVED] Graph question
whats the difference between say...

or what translation does it make to the graph? It was on a test I wrote but I was never really taught it. Is it like a reciprocal multiplied by 5? - February 24th 2009, 10:14 AMReckoner
- February 24th 2009, 10:19 AMbrentwoodbc
thanks(Yes)

- February 24th 2009, 10:26 AMbrentwoodbc
im trying to think of how you would find the invariant points.do you just go back to what the original equation was or?

like with 5/x what are the invariant points? I thought they had to be at 1/-1 - February 24th 2009, 10:28 AMReckoner
- February 24th 2009, 10:42 AMbrentwoodbc
I chose the wrong word, I mean how would you find the points to graph it?

like with the reciprocal of the line y=x the "vertex" of 1/x (if thats what it is called with reciprocals) is at (1,1) right. so with 5/x what would that point be? - February 24th 2009, 12:12 PMReckoner
I had typed up a response, but my browser crashed. Here:

I don't know if this is what you mean by "vertex," but usually the vertices of a curve are the points at which the derivative of its curvature is zero. The curvature of is

Differentiating,

So

and the vertices are at and

In general, the vertices of should be at and

Edit: I wasn't really thinking of this when I did the above, but the points along the axis of symmetry will be vertices, and is symmetric about the line So you could just find the points of intersection:

Much simpler!