From the graph, we can notice that the function is not defined at x = 1 and x = -3. A rational function is not defined when the denominator has a value of 0. From the given options, only option A is not defined at -3 and 1, as proven here
At x = -3
(-3)² + 2(-3) - 3 = 9 - 6 - 3 = 0
The denominator equals 0 at x = -3, then this function is not defined at x = -3
At x = 1
(1)² + 2(1) - 3 = 1 + 2 - 3 = 3 - 3 = 0
The denominator equals 0 at x = 1, then this function is not defined at x = 1
Then, the function y = x² - 1 / x² + 2x - 3 is the one of the graph. Then option A is the correct answer
