5.1 Polynomial Functions

5.1Polynomial Functions • Learning goals • graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. • graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.

monomial : a number, a variable, or the product of a real number and variables with whole number exponents polynomial : a monomial or the sum of monomials degree : • For a monomial – the sum of its exponents • For a polynomial – the largest sum of exponents from a term **Always put answers in standardform: descending order of exponents Vocabulary

By Degree • 0 – constant • 1 – linear • 2 – quadratic • 3 – cubic • 4 – quartic • 5 – quintic By # of Terms • 1 – monomial • 2 – binomial • 3 – trinomial • 4 or more - polynomial ClassifyingPolynomials Shape

Put in standard form • What is the degree of the polynomial? • Classify each polynomial by degree and number of terms • What shape is it? Ex 1

Write in standard form, classify, state degree and shape. Ex 2

The degree of a polynomial function affects • the shape of its graph • the maximum number of turning points • the way behaves at its ends turning point : places where a graph changes direction end behavior : direction of the graph where the arrows appear (far left and far right of the graph) Vocabulary

relative minimum /relative maximumpeaks and valleys within the graph of a polynomial that has several turning points Vocabulary

Find the relative minimum and maximum Ex 3

End Behavior

Ex 4 • Describe the end behavior • Is the graph odd or even? • Is the leading coefficient positive or negative? • Relative max or min?

Ex 5 • Describe the end behavior • Is the graph odd or even? • Is the leading coefficient positive or negative? • Relative max or min?

Ex 6 For each polynomial function: • describe the end behavior • sketch

Ex 7 For each polynomial function: • describe the end behavior • sketch

5.1 Polynomial Functions