Find the intercepts and asymptotes, use limits to describe the behavior at the vertical asymptotes. (37 and 39)

39)
Its always best to factorise where you can, in most questions it tends to be a necessary step and even if its not, it usually makes things easier;
In this case, you can factorise the denominator:


To get y-intercept/s, set x = 0 and solve:

y-intercept: (0, 1/12)

To get x-intercept/s, set y = 0 and solve:

x-intercept: (1, 0)

To find the asymptotes, it is necessary for us to have factorised the denominator so its a good thing that I did so at the beginning;

To get the vertical asymptote/s, set the denominator equal to 0, then just rearrange to get x:

vertical asymptotes: x = 4  and  x = -3

There are no horizontal asymptotes.