Why is it that average fix cost dominate that of the average total cost?

Answer 1

It doesn't always. You are probably looking at a manufacturing industry which is very capital intensive, meaning that there is lots of equipment or factories used in production. In a more service oriented business, more labor is likely to be used, and thus average variable cost would be the dominant portion of average total cost.

Answer 2

This statement is not true. It only dominates the decreasing part of the average total cost curve.
Your fixed cost if constant all the time, so as you move on producing more outputs, the AFC, average fixed cost consistently decreases. this is a force that pulls down the average total cost. However, we have some other forces that pushes up the the average total cost. MC is importantly related to your average variable cost, when your marginal cost is smaller than your average variable cost, your average variable cost, decreases, and when your marginal cost is smaller than your average variable cost, your average variable cost increases. Note, your Marginal cost and average variable cost decreases Note your marginal cost begins to slide down when you first started producing outputs, and it increase after a certain quantity. these forces combined together, we have a U-shaped average total cost curve. (Keypoint: ATC=AFC+AVC that is why the average total cost is affected by AFC and AVC)
It might be very confusing without a graphical illustration, but it is the basic idea in developing an average total cost curve. Hope it will help.