Transforming a function using a parent function

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SUMMARY

The discussion centers on transforming the function f(x) = (x² + 2x) / (2x + 2) into a recognizable parent function. The user initially considers the reciprocal function 1/x but realizes the degree of the numerator exceeds that of the denominator. A suggestion of using long division is provided as a method to simplify the function and identify a suitable parent function for transformation.

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  • Understanding of rational functions
  • Knowledge of polynomial long division
  • Familiarity with function transformations
  • Basic algebraic manipulation skills
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  • Study polynomial long division techniques
  • Research transformations of rational functions
  • Explore parent functions in algebra
  • Practice identifying transformations of various functions
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Students and educators in algebra, mathematicians focusing on function transformations, and anyone seeking to enhance their understanding of rational functions and their properties.

SwimmingGoat
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Ok, I've been working on a long problem (if you want all the steps I've taken to get to this point, I'll give them to you, but they aren't relevant, and I've done them correctly), and now I'm slightly stuck.

Right now I have f(x)=\frac{x^2+2x}{2x+2}. The current problem asks me if the graph can be defined as a transformation of some base function whose graph we already know. I'm having a hard time coming up with a parent function/graph that will help me transform to this equation. Any ideas or thoughts? I thought of doing the reciprocal 1/x, but the degree in the numerator is larger than the denominator...

Thank you in advance!
 
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Hi SwimmingGoat! :smile:

Hint: long division? :wink:
 
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aha! Thank you! I knew I was missing an obvious place to start. This is what happens when I do math for three hours straight...
 

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