How do I write the equation of a rational function given these characteristics

Question

1. $Y$ intercept at $-5$
2. No $x$ intercepts
3. Discontinuous points at $(-1,-5)$ and $(3, -5)$

This was on an assignment, please help! Edit: the graph is NOT linear

Answer 1

Hint: Discontinuous points come from common factors in the numerator and denominator, so you should be able to find two factors of the denominator from item 3. Since you have no $x$ intercepts, the function should not go through zero, and it sounds like you don't want vertical asymptotes. It looks like a nice graph that satisfies your needs would be the line $y=-5$ less the two discontinuous points.

Answer 2

$$y=\left(\frac{x+1}{\left| x+1\right|}\right)\left(\frac{x-3}{\left|x-3\right|}\right)-4$$