Question

Create a function that has 2 vertical asymptotes
a) provide an analysis for the behavior of the function around the vertical asymptotes.

Answer 1

y = 1/((x+1)(x-3))

make a rough sketch of the graph, then do the analysis.

copy and paste, delete the 2 spaces at the front before activating the link

h tt ps://www.wolframalpha.com/input?i=y+%3D+1%2F%28%28x%2B1%29%28x-3%29%29

The first graph shows only the bottom loops,
the second graph shows the full picture, I am sure you detect
the asymptotes

Answer 2

you might also want to consider
y = 1/((x+1)(x-3)^2)