To find the value of a + c, we can analyze the given information about the graph. Since the graph has a horizontal asymptote of y = 2, it means that as x approaches positive or negative infinity, the value of y approaches 2. This implies that the term ax + b/x + c approaches 2 as x approaches infinity.
On the other hand, the graph has a vertical asymptote at x = -3. This means that the term b/x approaches infinity as x approaches -3.
From these observations, we can conclude that the term ax approaches 2 as x approaches infinity, and the term b/x approaches infinity as x approaches -3. Therefore, in order for these two terms to balance each other out and approach a constant value, the coefficient a must be 0.
If a = 0, then the equation becomes b/x + c = 2. Since there are no other terms involving x, we can equate the constant terms on both sides, giving us b/x + c = 2.
From this equation, we can see that c = 2.
Therefore, a + c = 0 + 2 = 2.