3.2_Characteristics.Of.Polynomials

# 3.2_Characteristics.Of.Polynomials - Do all functions have...

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MHF 4U0 3.2 Characteristics of Polynomial Functions Equation and Graph Degree Even/Odd Degree? Leading Coefficient End Behaviours # of Turning Points Symmetry (Even/Odd) -∞ x x (a) x x x f 2 ) ( 3 - = (b) 1 3 4 2 ) ( 2 3 - - + - = x x x x f (c) 5 5 4 4 3 ) ( 2 3 4 + + - - = x x x x x f pg. 1/3

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MHF 4U0 Equation and Graph Degree Even/Odd Degree? Leading Coefficient End Behaviours # of Turning Points Symmetry -∞ x x (d) x x x x x f 2 2 ) ( 2 3 4 + + - - = (e) 5 18 3 7 2 ) ( 2 3 4 5 + - - + = x x x x x f (f) x x x x x x f 3 4 2 5 5 ) ( 2 3 4 5 + + - + - = pg. 2/3
MHF 4U0 3.2 Characteristics of Polynomial Functions Some Points to Ponder… 1. Compare the end behaviour of functions of odd degree with the end behaviour of functions of even degree. How can you determine the end behaviour by looking at the equation for the function? 2. How many turning points will a polynomial function of degree n have? 3. How many x -intercepts (roots/zeroes) will a polynomial function of degree n have? 4.
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Unformatted text preview: Do all functions have at least one zero? Why or why not? 5. Do all polynomial functions have an absolute maximum or absolute minimum? Explain. 6. Is every function of even degree an even function? Why or why not? 7. Is every function of odd degree an odd function? Why or why not? 8. Can an even function have odd degree? Can an odd function have even degree? Example #1: For each of the functions listed below: (a) describe the end behaviour (b) discuss the possible number of turning points and zeroes (c) sketch a possible graph of the function (i) 1 2 ) ( 2 4 + + = x x x f (ii) x x x g 3 ) ( 5--= (iii) 5 2 3 ) ( 2 3--+ = x x x x h Assigned Work: page 136 #1 – 3, 4abde, 5 (pair share), 6ac, 7bd, 8, 9, 12 pg. 3/3...
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3.2_Characteristics.Of.Polynomials - Do all functions have...

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