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# For how many values of x is the function

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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
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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
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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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