On the interval $(0,15),$ locate the points where the function $f$ has discontinuities. For each discontinuity, indicate which continuity conditions are not met.

• A. $a=0,$ the function is discontinuous because ${\lim }_{x\to a}f\left(x\right)\ne f\left(a\right)$; $a=15,$ the function is discontinuous because the limit does not exist
• B. $a=3,$ the function is discontinuous because the limit does not exist; $a=10,$ the function is discontinuous because ${\lim }_{x\to a}f\left(x\right)\ne f\left(a\right)$
• C. $a=3,$ the function is discontinuous because ${\lim }_{x\to a}f\left(x\right)\ne f\left(a\right)$; $a=10,$ the function is discontinuous because the limit does not exist
• D. $a=0,$ the function is discontinuous because ${\lim }_{x\to a}f\left(x\right)\ne f\left(a\right)$; $a=10,$ the function is discontinuous because the limit does not exist

Answer: (C)