The painter used a thin brush to paint the foliage in the background.

Respectable painters could do both. Of direction, they use a "reputable" spray gun or the nice of brushes depending on their prefference. In the event that they spray they still will use a brush for "slicing" and trimming. Some may even use a roller alternatively of spray or brush. The change is the "pro's" do a good/appropriate job of PREP. They be certain paint is clean and loose paint is eliminated then bare wooden is properly primed. If they do not do a excellent prep job then they don't seem to be rather professionals!

 But to answer this question, it would be an infinitive phrase. 

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The image explain. how in the late 1900. sugar spread to the world