Final answer:
The vertical asymptote of the function f(x) = log₅ x + 4 occurs at x=0, as the log function is undefined for non-positive values.Now, to find the upper and lower cutoff frequencies, we use the fact that the bandwidth is the difference between these two frequencies.
Step-by-step explanation:
The vertical asymptote of the logarithmic function f(x) = log₅ x + 4 can be determined by finding the value of x that makes the function undefined, which is the point where the input to the log function is zero. Since the log function is only defined for positive values, the vertical asymptote occurs at x=0. This is because as the value of x approaches zero from the right, the value of f(x) decreases without bound, approaching negative infinity.