Final answer:
The behavior of the function f(x) = -log(3x-5) + 6 as x approaches its vertical asymptote x = 5/3 is that f(x) will approach negative infinity from the right side since the logarithm of a value approaching zero from the positive side becomes increasingly negative.
Step-by-step explanation:
The question asks about the behavior of the function f(x) = -log(3x-5) + 6 as x approaches the vertical asymptote. The vertical asymptote for a logarithmic function like this one occurs where the argument of the logarithm is zero. So for our function, the vertical asymptote will be at x = 5/3, since that makes the term 3x - 5 equal to zero.
As x approaches the vertical asymptote from the right, the 3x - 5 term becomes very small (approaches zero), making the -log(3x-5) term increasingly negative, which in turn makes f(x) increasingly large because we subtract a negative (which is the same as adding a positive). Therefore, as x approaches 5/3 from the right, f(x) will approach negative infinity. From the left of 5/3, x cannot exist because then 3x - 5 would be negative, and the logarithm of a negative number is undefined in real numbers.