section 3.2: polynomial functions · 2019. 12. 17. · section 3.4: the real zeros of a polynomial...
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60 Part 1: Video Notebook
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Section 3.2: Polynomial Functions
Key Topics: polynomial functions, power functions, end behavior, end term test, leading-term test, zeros, multiplicity, turning points, Intermediate Value Theorem, graphing techniques
A graph of a polynomial function is a __________ and ____________ curve.
Describe power functions of even degrees.
Describe power functions of odd degrees.
Chapter 3: Polynomial and Rational Functions 61
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62 Part 1: Video Notebook
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Use the leading-term test to determine the end behavior of the graph of 4 3 2( ) 3 7 5 8 11. f x x x x x
(a) as and as y x y x (b) as and as y x y x (c) as and as y x y x (d) as and as y x y x
Chapter 3: Polynomial and Rational Functions 63
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64 Part 1: Video Notebook
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Sketch the graph of ( ) 2( 1)( 2)( 3). f x x x x
Chapter 3: Polynomial and Rational Functions 65
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Section 3.3: Dividing Polynomials
Key Topics: polynomial factor, division algorithm, synthetic division, remainder theorem, factor theorem
Compare/contrast long division and synthetic division by dividing 3 26 32 x x x by 5.x
66 Part 1: Video Notebook
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Given that 5 is a zero of the function 3 2( ) 4 11 54 45, f x x x x solve the polynomial equation 3 24 11 54 45 0. x x x
Chapter 3: Polynomial and Rational Functions 67
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Section 3.4: The Real Zeros of a Polynomial Function
Key Topics: Rational Zeros Theorem, Conjugate Pairs Theorem, Descarte’s Rule of Signs, Rules for Bounds on the Zeros
68 Part 1: Video Notebook
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Find all rational zeros of the polynomial 4 3 28 4 48 P x x x x x .
Chapter 3: Polynomial and Rational Functions 69
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Section 3.5: The Complex Zeros of a Polynomial Function
Key Topics: Fundamental Theorem of Algebra, Factorization Theorem for Polynomials, Number of Zeros Theorem, Conjugate Pairs Theorem, Odd-Degree Polynomials, Factorization Theorem for a Polynomial with Real Coefficients
70 Part 1: Video Notebook
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Find all zeros of the polynomial 4 3 28 4 48 P x x x x x .
Chapter 3: Polynomial and Rational Functions 71
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Section 3.6: Rational Functions
Key Topics: rational functions, vertical asymptotes, horizontal asymptotes, graphing techniques
Find the domain of the rational function 21
6xf x
x x
.
72 Part 1: Video Notebook
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Find all vertical asymptotes of the rational function 2125
xf xx
.
Find the horizontal asymptote of the graph of the rational function 6 53 7xf x
x.
Determine the oblique asymptote for 3
23( )1
x xf xx
Chapter 3: Polynomial and Rational Functions 73
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Sketch the graph of 2 9( )
2
xf xx
74 Part 1: Video Notebook
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Section 3.7: Variation
Key Topics: variation relationships—direct, inverse, joint, combined
Suppose y is directly proportional to x, and 40y when 10x . Find y if 16x .
Suppose y varies inversely as x, and 12y when 6x . Find y if 8x .
Chapter 3: Polynomial and Rational Functions 75
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