Question

How do you graph `y=(2x^2-9x-5)/(x^2-16)` using asymptotes, intercepts, end behavior?

Answer 1

The vertical asymptotes are `x=4` and `x=-4`
And the horizontal asymptote is `y=2`

Explanation:

Factorising numerator and denominator
`y=((2x+1)(x-5))/((x+4)(x-4))`
To factorise you can use the formula`x=(-b+-(b^2-4ac))/(2a)`
We can see that `x!=+-4` as we cannot divide by 0. Hence we obtain the vertical asymptotes `x=4` and `x=-4`
And the limit of y as `x->oo` is 2. therefore the horizontal asymptote is `y=2`
When `x=0` , `y=5/16`
graph{(2x^2-9x-5)/(x^2-16) [-20, 20, -10, 10]}