Question

State the domain of 1b, then determine the equation of any vertical asymptotes and/or coordinates of any holes in the graph of the function.

Answer 1

We have

$f(x)=\frac{2x^2+x}{x^2-5x+6}$

First we will factorize the function

$f(x)=\frac{x(2x+1)}{\mleft(x-2\mright)(x-3)}$

The domain is

$\: \mleft(-\infty\: ,\: 2\mright)\cup\mleft(2,\: 3\mright)\cup\mleft(3,\: \infty\: \mright)$

In this case, we have two vertical asymptotes

x-2=0

x=2

x-3=0

x=3

ANSWER

The domain is

$\: \mleft(-\infty\: ,\: 2\mright)\cup\mleft(2,\: 3\mright)\cup\mleft(3,\: \infty\: \mright)$

The vertical asymtotes

x-2=0

x=2

x-3=0

x=3