I'm unfamilar with this rates of change question.

Let f be the function f:D -> R , f(x)=loge(3-4x) where D is the largest domain over which f is defined.

Use calculus to show that the rate of change of f(x) with respect to x is always negative.

I have no clue on how to do this, any help would be appreciated.

What do you mean by f(x)=loge(3-4x) ?

f(x) = log e^{(3-4x)}

Then, if you differentiate f(x) with respect to x, you'll find that the rate of change is always negative. You can substitute x in the differentiation by infinity and negative infinity to check your answer.