Graph Transformations: y=1/x to y=x+3/x+1 & y=2x/x-1

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To transform the graph of y=1/x to y=(x+3)/(x+1), a vertical shift and horizontal shift are required. The transformation involves shifting the graph left by 1 unit and up by 3 units. For the graph of y=2x/(x-1), the transformation includes a vertical stretch by a factor of 2 and a horizontal shift right by 1 unit. Proper use of parentheses is crucial for clarity in mathematical expressions. Understanding these transformations is essential for accurately interpreting and solving precalculus problems.
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Describe the transformation on the graph of y=1/x needed to obtain the graph of each of the following:

a) y= x+3/x+1

b) y= 2x/x-1

im stuck on how to answer this question...how would i solve this?...thanks
 
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Learn to use parentheses. It is important, and you seem like a kindergarten pupil when forgetting them.
 
Most peope would interpret x+3/x+1 as x+ (3/x)+ 1. I suspect that you mean (x+3)/(x+1).

Most people would interpret 2x/x-1 as (2x/x)- 1= 2- 1= 1. I strongly suspect that you mean 2x/(x-1).

I would also point out that these look a lot like homework. I'm moving this thread to the "precalculus homework" forum.
 

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