What is the Point Discontinuity Problem in Rational Functions?

AI Thread Summary
The discussion revolves around identifying the value of p that causes a discontinuity in the rational function f(x) = (x^2 - 6x + 9) / (x - p). A discontinuity occurs when the denominator equals zero, which means p must equal the x-value that makes the denominator zero. Participants emphasize the importance of understanding the function's behavior and suggest reviewing relevant material for clarity. Ultimately, the original poster successfully solved the problem after receiving guidance. The conversation highlights the need for a solid grasp of rational functions to address discontinuities effectively.
neuro.akn
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Homework Statement



Find the value of p at which the discontinuity would occur.


Homework Equations



f(x) = x^2 - 6x + 9 / x - p

The Attempt at a Solution



Able to solve if p has an assigned numerical value, but help is needed for determining the value of p at which the discontinuity would occur. Any help is appreciated. Thank you.
 
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Factorize x^2 - 6x + 9.
 
Okay. Thanks; once I have done that, how would I solve for p?
 
If you haven't yet found the answer to your other problem, I would suggest you do that and then come back to this problem, at which point the solution will hopefully be obvious.

In any event I would recommend re-reading the material on which these problems are based, since you don't seem to be fully comfortable with it.
 
A discontinuity occurs when you cannot determine the function value at a certain argument(x) value. There's an operation only Chuck Norris can do..or so they say.

X-p , you know that there is one value that it can't have since it's in the denominator.
You also know that the function at 1st glance Could be 0 when X=?? according to the numerator.

What's the 1 value that cannot be P? Everything else can. Think of a hyperbole.
 
Last edited:
neuro.akn said:

Homework Statement



Find the value of p at which the discontinuity would occur.


Homework Equations



f(x) = x^2 - 6x + 9 / x - p

The Attempt at a Solution



Able to solve if p has an assigned numerical value, but help is needed for determining the value of p at which the discontinuity would occur. Any help is appreciated. Thank you.

As in your other posting: you need parentheses! If I read what you wrote using standard rules for mathematical expressions, I would see
f(x) = x^2 - 6x + \frac{9}{x} - p.
 
Last edited:
Ray Vickson, (x^2 - 6x + 9) / (x - p)
Thank you all for your help.
 
The thing is, we have not gone over this material at all.
 
I have solved the problem. Thank you everyone.
 

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