Question

How do you determine the vertical and horizontal asymptotes of the graph of each function `h(x) = (x+6)/(x^2 - 36)`?

Answer 1

Vertical asymptotes occur at the points where the function tends to infinity (positive or negative). In case of this function these are points where the denominator equals to zero, that is `x=6` and `x=-6`.

Horizontal asymptotes exist if the function tends to some constant as its argument tends to infinity (positive or negative). In this case, when `x->+-oo`, function tends to zero, so the X-axis is the horizontal asymptote for both directions of infinity for its argument.