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3-3 Properties of Functions

3-3 Properties of Functions - 3-3 More About Functions...

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3-3: More About Functions Increasing and Decreasing functions; A function f is increasing on an open interval I if, as x increases,  f(x) also increases.  It is decreasing if, as x increases, f(x) decreases.  It is constant if, as x increases, f(x)  remains the same. Local Maximum;       Local Minimum:       In non-technical language, a  local minimum  is a turning point in the  graph where f(x) is decreasing on the left of point c and increasing on the right side of a point c.  Point c  is a local maximum if the graph is increasing on the right and decreasing on the left. Even and Odd Functions:    On the graph,  even  functions are symmetric to the y-axis; that is, for every point  (x, y), there is also a point (-x, y) on the graph.   Odd  functions are symmetric to the origin; that is, for  every point (x, y), there is also a point (-x, -y).  From equations:  A function is even if f(-x) = f(x).  It is

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3-3 Properties of Functions - 3-3 More About Functions...

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