Algebra

What are the equations of the asymptotes of the graph of  \(f(x)=\frac{3}{x-2}+9\)

Set the denominator equal to zero to find the equation of an asymptote.

x - 2  =  0

x  =  2

To find the other asymptote, let's first solve for  x .

y  =   3 / (x - 2) + 9

y - 9   =   3 / (x - 2)

(x - 2)(y - 9)   =   3

x - 2   =   3 / (y - 9)

x  =   3 / (y - 9) + 2

Now set this denominator equal to zero to find the equation of the other asymptote.

y - 9  =  0

y  =  9