Section 2.3: Polynomial Functions of Higher Degree with Modeling

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Presentation transcript:

Section 2.3: Polynomial Functions of Higher Degree with Modeling Find f(g(x)) and g(f(x)) given f(x) = 2x + 1 and g(x) = 1 + 3x x - 3 x – 2 What does the composites tell you about f(x) and g(x)?

General Shape of Polynomial Functions

Standard vs. Factored Form General Shape Y-intercept General Shape X-intercept(s) Standard vs. Factored Form

Multiplicities of Zeros Multiplicity of 1 Multiplicity of 2 Multiplicity of 3 Multiplicities of Zeros

Identifying Degrees and Zeros

Solve.

Zeros: -6, 1, 9 Zeros: Given the zeros, write an equation for each polynomial in standard form.

Mix-and-Match Activity If you were given a card with zeros, write the equation for the polynomial in standard form. If you were given a card with an equation of a polynomial, determine the zeros of the function. NOW, find the person that you match up with. Mix-and-Match Activity