Chapter 3 – Polynomial Functions ● 1 Pre-Calculus 12 Characteristics of Polynomial Functions Definition A function of the form 0 1 1 2 2 2 2 1 1 ... ) ( a x a x a x a x a x a x f n n n n n n + + + + + + = − − − − , where n is a ___________________________, x is a _______________ and 0 1 2 2 1 , , ,..., , , a a a a a a n n n − − are _____________ ______________. n a is called the leading coefficient, and 0 a is the constant term. Example 1: Which functions are polynomials? Justify your answer. If they are polynomials, state the degree, the leading coefficient, and the constant term of each polynomial functions. Polynomial Polynomial? Yes/No Degree Leading coefficient Constant term 5 ) ( + = x x f _______ _______ _______ _________ 4 3 ) ( x x g = _______ _______ _______ _________ x y = _______ _______ _______ _________ 1059 7 . 0 2 3 2 3 4 + − + − = x x x x y _______ _______ _______ _________ 5 1 9 . 0 3 2 ) ( 2 + − = x x x f _______ _______ _______ _________ x x h 1 ) ( = _______ _______ _______ _________ 7 ) ( 2 1 − = x x g _______ _______ _______ _________ 3 4 4 4 + − − = x x y _______ _______ _______ _________ Characteristics of Polynomial Functions: Polynomial functions and their graphs can be analysed by identifying the _________________, ____________________, _____________________________, and the _____________________________________. Definition: end behaviour – the behaviour of the __________________ of the function as x-values become ___________________________________
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Chapter 3 – Polynomial Functions ● 1
Pre-Calculus 12
Characteristics of Polynomial Functions
Definition
A function of the form 01
12
22
21
1 ...)( axaxaxaxaxaxf nn
nn
nn ++++++= −
−−
− ,
where n is a ___________________________, x is a _______________ and 01221 ,,,...,,, aaaaaa nnn −− are
_____________ ______________. na is called the leading coefficient, and 0a is the constant term.
Example 1: Which functions are polynomials? Justify your answer. If they are polynomials, state the
degree, the leading coefficient, and the constant term of each polynomial functions.