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

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SUMMARY

The discussion focuses on the transformation of the graph of the function y=1/x to the functions y=(x+3)/(x+1) and y=2x/(x-1). Participants emphasize the importance of using parentheses to clarify expressions, as misinterpretation can lead to incorrect conclusions. The correct transformations involve understanding rational functions and their graphical representations. The conversation highlights common pitfalls in algebraic notation that can confuse the intended mathematical operations.

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  • Understanding of rational functions
  • Knowledge of graph transformations
  • Familiarity with algebraic notation and parentheses usage
  • Basic skills in precalculus concepts
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  • Study graph transformations of rational functions
  • Learn how to properly use parentheses in algebraic expressions
  • Explore the characteristics of asymptotes in rational functions
  • Practice problems involving transformations of y=1/x
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Students studying precalculus, educators teaching graph transformations, and anyone looking to improve their understanding of rational functions and algebraic notation.

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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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