Continuity and Discontinuity

AP Calculus AB· difficulty 1/5

A function is continuous at x=ax = a on a graph when

  • A

    The function is differentiable at x=ax = a

  • B

    The graph has no break at x=ax = a

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  • C

    The function has a horizontal tangent at x=ax = a

  • D

    The function attains its maximum at x=ax = a

Explanation

Continuity means the graph can be drawn through the point without lifting the pencil — no jumps, holes, or asymptotes.

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