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.
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.
Larry Green (Lake Tahoe Community College)
Integrated by Justin Marshall.