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)=(2x^2+x)/(x^2-5x+6)`

First we will factorize the function

`f(x)=(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