ANSWER
The answer is B.
[tex]y = \frac{ {x}^{2} - 1}{ {x}^{2} + 2x - 3 } [/tex]
EXPLANATION
The graph represents a rational function.
This rational function has a hole at x=1 and a vertical asymptote at x=-3.
This implies that the denominator of the rational function in factored form is
[tex](x + 3)(x - 1)[/tex]
When we expand this, we get:
[tex] {x}^{2} + 2x - 3[/tex]
This tells us that the answer must be option B.
This graph also has a horizontal asymptote at y=1.
The numerator must therefore have leading term that is quadratic with the coefficient being unity or 1.
Therefore the function is actually
[tex]y = \frac{ {x}^{2} - 1}{ {x}^{2} + 2x - 3 } [/tex]
