Final answer:
The degree of the given function is 1.
Step-by-step explanation:
The degree of a polynomial function is determined by the highest power of x in the function. In this case, the function f(x) = ((x+5)(x-2)(x-7))/((x+9)(x-6)) can be simplified as follows:
f(x) = (x+5)(x-2)(x-7) / (x+9)(x-6)
The highest power of x in the numerator is x^3, and the highest power of x in the denominator is x^2. Therefore, the degree of the function f(x) is 3 - 2 = 1.