can anyone tell me the solution with full explanation

Suppose f is a continuous real-valued function defined on the closed interval [0,1]. Which of the following must be true?

1. There is a constant C>0 such that |f(x)-f(y)|<= C for all x and y in [0,1]

2. There is a constant D>0 such that |f(x)-f(y)|<= 1 for all x and y in [0,1] that satisfy |x-y|<=D

3. There is a constant E>0 such that |f(x)-f(y)|<= E|x-y| for all x and y in [0,1]

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