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For how many values of  x is the function \(y=\frac{x-2}{x^2-7x+10}\)

tertre  Mar 5, 2017
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 #1
avatar+1227 
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Please help!!!!!!!!!!!!!!

tertre  Mar 5, 2017
 #2
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I am assuming that you mean 

For how many values of x is the function \(y=\dfrac{x-2}{x^2-7x+10}\) undefined?

 

As the denominator is a quadratic function, there are values of x which makes the function \(y=\dfrac{x-2}{x^2-7x+10}\) undefined.

MaxWong  Mar 5, 2017
 #3
avatar+91259 
+5

 

 

For how many values of  x is the function     

 

 

\(y=\frac{x-2}{x^2-7x+10}\;\;\text{undefined}\)

 

\(y=\frac{x-2}{(x-2)(x-5)} \)

 

you cannot divide by zero so x cannot be 2 or 5.   this graph will have holes or asyptotes.

 

So this is fucntion for all real values of x except for x=2 and x=5

 

It will be a function in the following domain.

(-infiny,2), (2,5), (5,infity)

 

cancel down and you get

 

\(y=\frac{1}{x-5}\\ \)

This is a hyperbola.  The asyptotes are x=5 and y=0 but there will be a hole at (2,-1/3)

 

here is the graph:

 

Melody  Mar 5, 2017

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