3.4: Polynomials and Graphs

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Oct 6, 2021
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- 3.3: Polynomial Equations
- 3.5: Rational Functions

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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.

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1. Left and Right Behavior

2. Max and Min

3. Three Step Procedure For Graphing Polynomials

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