#2**0 **

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 **2 **values of x which makes the function \(y=\dfrac{x-2}{x^2-7x+10}\) undefined.

MaxWong
Mar 5, 2017

#3**+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