We need to construct a rational graph with the data in the picture. So, the drawing is some like this:
In the picture above, the vertical asymptotes are yellow, the horizontal asymptote is in green, and a possible rational function is in red.
The points (0, -5) and (-5/3, 0) belong to the function.
When the function approach to x=0.5 from the right goes to -infinity, that is the limit.
When the function approach to x=0.5 from the left goes to infinity, that is the limit.
When the function approach to x=1 from the right goes to infinity, that is the limit.
When the function approach to x=1 from the left goes to infinity, that is the limit.
And when the function goes to x = -infinity or x=infinity the functions approach to the horizontal asymptote y=3/2.
You can see in the picture this behaviour of the red line.
