How would I describe and correct the error given the function f(x)=3x-5? The error resides in the following: f(1)=1/3-4/3(1) =1/3-4/3 =-3/3 =-3

This question is a bit unclear, but I will assess what I see as the errors in the equation above.

f(x) = 3x-5

This is a standard and simple algebraic equation. If you want to determine f(1), you simply insert 1 in the place of x in the above equation.
Therefore f(1) = 3(1) - 5, or 3 - 5 = -2. If this is what is being explored, then f(1) = -2.
The second set of equations, however, seems to be following f(x) = 1/3 - 4/3(x), which is an entirely different equation. In that instance, f(1) = 1/3 - 4/3 = -1
If you are trying to reduce the initial equation by dividing by 3 throughout, you would have f(x) = x - 5/3, and when plugging in x = 1, you end up with -2/3. Multiply through by 3 again to return to the initial equation and the final result is the same: f(1) = -2.
I'm not sure if this is exactly what you're looking for, but I hope this helps a little bit.