Question

How do you find the domain of `f(x) = ( 9x+8)/(-9-8x)`?

Answer 1

Start by finding the 'forbidden' values of `x`

The denominator of a fraction may not be zero, so let's see when it is:
`-9-8x=0->-9=8x->x=-9/8`
Answer : `x!=-9/8`
This forms a vertical asymptote:
graph{(9x+8)/(-9-8x) [-10, 10, -5, 5]}

Extra : as you can see, there is also a horizontal asymptote at

`y=-9/8`. This has to do with the range of this function