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Calculus 1

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Math Video Library Collection

Graphs of Basic Functions and Relations; Symmetry

Video Summary:

Continuity (Informal Definition) A function is continuous over an interval of its domain if its hand-drawn graph over that interval can be sketched without lifting the pencil from the paper. Discontinuity If a function is not continuous at a point, then it may have a point of discontinuity, or it may have a vertical asymptote. Increasing The range values increase from left to right The graph rises from left to right Decreasing The range values decrease from left to right The graph falls from left to right To decide whether a function is increasing, decreasing, or constant on an interval, ask yourself “What does the graph do as x goes from left to right?” If we were to “fold” the graph of f (x) = x2 along the y-axis, the two halves would coincide exactly. We refer to this property as symmetry.



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