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WebGraphing.com Forum » List all forums » » Forum: Precalculus and Trigonometry Homework Help » » » Thread: Rational Functions |
| Posted by 2446 at Nov 14, 2011 2:55:54 PM |
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Rational Functions I am trying to help my grade 12 son with a math assignment relating to rational functions. Is there such a thing as a rational function that has a horizontal asymptote that lies above the x-axis, has exactly 2 holes, has at least one vertical asymptote, touches the x-axis exactly twice, the instantaneous rate of change at x=3 is postitive, has even symmetry, passes through the point (1, 10)???? Hoping there is a math whiz reading this. Thanks! |
| Posted by EdwardCasey at Dec 12, 2011 4:24:29 AM |
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Re: Rational Functions A rational function is by definition the quotient of two polynomials.You can get the solution and take nearest rational value of result.May be it will near to your solution. ---------------------------------------- Roller Blockout Blinds |
| Posted by pskinner at Dec 12, 2011 5:25:07 PM | ||
Re: Rational Functions
This is a function that needs to be built. For symmetry with one vertical asymptote, you can use the factor of x^2 in the denominator so that x=0 is the sole vertical asymptote. For symmetry with two holes, you can have the factor (x^2-a^2), a>0, in both the numerator and denominator to create holes as x=+a and x=-a. To have it cross the x-axis exactly twice with and pass through (1,10), you could use -10/x^2. This function also has the property that at x=3, a<>3, it has a positive slope [this is equivalent to have a positive instantaneous rate of change]. ---------------------------------------- Principal Skinner |
| Posted by phonesystems at Dec 13, 2011 2:10:36 AM |
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Re: Rational Functions To get more best example visit this site which gives demo of all the required one.. http://demonstrations.wolfram.com/InstantaneousRateOfChangeExploringMoreFunctions/ ---------------------------------------- broadband for business |