Question

Describe the vertical asymptote (s) and hole(s) for the graph of y= (x-3)(x-1)/(x-1)(x-5)

Answer 1

In the denominator of the fraction is given expression $(x-1)(x-5).$ This means that

$x\neq 1,\\x\neq 5.$

Now simplify the expression $y=\dfrac{(x-3)(x-1)}{(x-1)(x-5)}:$

$y=\dfrac{(x-3)(x-1)}{(x-1)(x-5)}=\dfrac{x-3}{x-5}.$

This means that $x=5$ is the equation of vertical asymptote and, therefore, since function id not defined for $x=1$ this point is hole of the function.