Final Answer:
The function corresponding to the given graph with an asymptote at -5 is f(x) = a / (x + 5), where 'a' is a constant.
Step-by-step explanation:
The presence of an asymptote at -5 in the graph indicates that the function approaches infinity as x approaches -5. This behavior is characteristic of rational functions with a denominator of (x + 5), as dividing by zero at x = -5 results in an undefined value. Therefore, the general form of the function is f(x) = a / (x + 5).
To determine the value of 'a,' additional information from the graph or the context of the problem is needed. The constant 'a' will affect the vertical stretch or compression of the graph and its precise location relative to the asymptote. Without specific details, 'a' remains a parameter that can be adjusted based on the specific characteristics required for the function.
In summary, the function corresponding to the given graph is f(x) = a / (x + 5), where 'a' is a constant yet to be determined. This rational function exhibits an asymptote at -5, capturing the behavior of the graph as x approaches that value. The exact nature of the function, including the specific value of 'a,' would be determined by additional information or constraints provided in the problem.