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For a function to be continuous at an interior point $a$, three conditions must be met: first, the function value $f(a)$ must be defined; second, the two-sided limit $\lim_{x \to a} f(x)$ must exist; and third, this limit must equal the function value $f(a)$. When checking the limit for piecewise functions, you must evaluate the correct branch on each side of $a$.

Conditions: The point $a$ is an interior point of the domain.; The function is defined piecewise or has branches around $a$.

For a function to be continuous at an interior point $a$, three conditions must be met: first, the function value $f(a)$ must be defined; second, the two-sided limit $\lim_{x \to a} f(x)$ must exist; and third, this limit must equal the function value $f(a)$. When checking the limit for piecewise functions, you must evaluate the correct branch on each side of $a$.

Conditions: The point $a$ is an interior point of the domain.; The function is defined piecewise or has branches around $a$.