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(C) The graph represents the function $f(x) = |x-1|$.At $x=1$,the graph is continuous because there is no break in the curve.However,at $x=1$,there is

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Continuous but not differentiable at $x=1$

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(C) The graph represents the function $f(x) = |x-1|$.At $x=1$,the graph is continuous because there is no break in the curve.However,at $x=1$,there is a sharp corner (or cusp),which means the left-hand derivative and right-hand derivative are not equal.Specifically,the left-hand derivative is $-1$ and the right-hand derivative is $1$.Therefore,the function is continuous but not differentiable at $x=1$.

The function represented by the following graph is,

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