How to sketch y=(-3x^2 +1)/(x^2)

Thread starter TyErd
Start date Feb 10, 2010
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SUMMARY

The discussion focuses on sketching the graph of the function y=(-3x^2 +1)/(x^2). The transformation of the function is simplified to y=-3 + (1/x^2), allowing users to leverage the known graph of y=(1/x^2) for accurate sketching. This method highlights the relationship between the original function and its components, facilitating a clearer understanding of its behavior.

PREREQUISITES

Understanding of rational functions
Familiarity with graph transformations
Knowledge of the function y=(1/x^2)
Basic algebraic manipulation skills

NEXT STEPS

Study graph transformations of rational functions
Explore the properties of y=(1/x^2) and its asymptotic behavior
Learn about sketching techniques for polynomial functions
Investigate the effects of coefficients on the shape of rational functions

USEFUL FOR

Students in calculus, mathematics educators, and anyone interested in mastering the sketching of rational functions and their transformations.

Feb 10, 2010

TyErd

How to sketch y=(-3x^2 +1)/(x^2)

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Feb 10, 2010

Mentallic

Homework Helper

Similar deal to your hyperbola question you made previously.

[tex]\frac{-3x^2+1}{x^2}=\frac{-3x^2}{x^2}+\frac{1}{x^2}=-3+\frac{1}{x^2}[/tex]

so now you should be able to sketch the graph using already known graphs such as [itex]y=\frac{1}{x^2}[/itex]