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Unformatted text preview: from a decreasing function to an increasing function). 1 2 The Zeros of a polynomial r a (real) zero of f , or root of f , or an xintercept of the graph of f means that • f ( r ) = 0, r is a REAL number. • ( xr ) is a factor of f . Example 2 Example 3 Example 4 2 3 Multiplicity r is a zero of multiplicity m of f if • ( xr ) m is a factor of f . • ( xr ) m +1 is NOT a factor of f . Then ﬁnd the degree of the polynomial. r is a zero of EVEN multiplicity : • Graph TOUCHes the xaxis at r . • Sign of f does NOT change from one side to the other side of r . r is a zero of ODD multiplicity : • Graph CROSSes the xaxis at r . • Sign of f changes from one side to the other side of r . Figure 2: The graph of y = f ( x ) = ( x + 1) 2 ( x )( x1)( x2) 2 3 Example 6 Example 7 Example 8 4...
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 Spring '11
 Nuegyen
 Complex number

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