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3.4: Polynomials and Graphs

  • Page ID
    236
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    1. Left and Right Behavior

    We will investigate the outer shape of several polynomials and explore the following rules:

    Even Odd
    Pos UU DU
    Neg DD UD


    Where Even and Odd refers to the degree of the polynomial, Pos and Neg refers to the leading coefficient, And a U or a D refers to the left and right behavior of the curve.

    alt

    2. Max and Min

    Theorem

    If \(f(x)\) is a polynomial of degree \(n\) then \(f(x)\) has at most \(n - 1\) relative extrema.

    Where relative extrema are "lumps" of the graph.

    has at most 4 relative extrema.

    3. Three Step Procedure For Graphing Polynomials

    Step 1: Factor the polynomial into linear factors of the form

    \[ax + b\]

    Step 2 : Determine the left and right behavior of the graph and the shape of the graph near each \(x\) intercept.

    Step 3: Connect the dots.

    alt

    Larry Green (Lake Tahoe Community College)

    • Integrated by Justin Marshall.


    This page titled 3.4: Polynomials and Graphs is shared under a not declared license and was authored, remixed, and/or curated by Larry Green.

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