How did the rise of huge industrial cartels affect free market competition?

Cartels could fix prices and sell at a loss to strangle out competition. Then raise prices afterward which would cover all previous losses. 
They could generate income by horizontal integration which would be possibly controlling all retail sales of a certain product. 
They could also generate income through vertical integration which meant owning a large portion of the industry (possibly mining) which provided the raw material, the means of production (factories, for example), the means of transporting the product to market (rail roads for example), and even owning the means of selling the product(s) (retailing). They could set the price and costs all along the way. They could also exploit their workers by being the 'only show in town' and therefore setting wages low and working hours high. If a vertically integrated company had to show their books to government auditors they could try to make a case to show a small advantage over competitors at each level of their operation which would come out overall as a major advantage which could put others out of business. 
A couple of industries to look at would be the railroads and oil. People to research: Andrew Carnegie, J. D. Rockefeller and other industrialists/robber barons. A student may want to read the works of some of the 'muckrakers' of the era.