Without carbohydrate in the broth (some) bacteria would then degrade the peptone, which from its end products would increase pH and then turn zhe phenol red pink. So I think this is some type of control just to make sure the test parameters can produce a pink broth. Is there something more here that I'm missing though? The question is asking what function phenol red broth without carbs serves, and that's only thing I can think of. Is this correct or is there something else that is more relevant?