Notes 4.3 Graphs of Polynomial Functions Basic polynomial shapes: The graphs of polynomial functions of the form f(x) = axn, with n  2, are two basic types, odd or even depending on the degree of the function.

Properties of General Polynomial Functions: Every graph of a polynomial function is continuous; it is an unbroken curve with no jumps, gaps or holes. Graphs of polynomial functions have no sharp corners.  

End Behavior: When a polynomial function has odd degree, one end of its graph shoots upward and the other end downward. When a polynomial function has even degree, both ends of its graph shoot upward or both shoot downward.  

Ex. 1 Determine if the graph represents and even or odd function & whether a is positive or negative.

Intercepts: The graph of a polynomial function of degree n: has one y-intercept, which is equal to the constant term has at most n x-intercepts   Multiplicity: Let c be a zero of multiplicity k of a polynomial f: If k is odd, the graph of f CROSSES the x-axis at c. If k is even, the graph of f TOUCHES or BOUNCES, but does not cross, the x-axis at c.

Ex. 2 Write an equation in factored form to describe the given graph.

2b.

Ex. 3 Write an equation in factored form using the given information. a. f(x) is of degree 5, y –intercept is (0, 2), zeros: 1 (multiplicity 3), 2 (multiplicity 2)

b. f(x) is of degree 4, y intercept is (0, -16), zeros: -2 (multiplicity 3), and 1