Final answer:
The function y = 3/(x - 4) + 2 has no holes because there is no common factor that can be canceled in the numerator and denominator. There is a vertical asymptote at x = 4, where the function is undefined.
Step-by-step explanation:
Finding the Holes of a Rational Function
The function y = 3/(x - 4) + 2 is a rational function, which is a function that is the ratio of two polynomials. A hole in the graph of such a function occurs when there is a common factor in the numerator and denominator that can be canceled but originally set the denominator to zero. In this case, there is no factor in the numerator that can be canceled with x - 4 in the denominator. Therefore, there is no hole in the graph due to cancellation. However, there will be a vertical asymptote at x = 4, because that is where the denominator would be zero and the function undefined. We must also check for any potential values that could cause the numerator to be zero, but since the numerator is a constant, 3, it does not have any zeros. Hence, the correct answer for the location of any holes is option a) No holes.