+4609 For how many values of x is the function \(y=\frac{x-2}{x^2-7x+10}\)
+9519 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.
+118608
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:
