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MATA30H3 (41)
Lecture

# unit 1 to 2.docx

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Department
Mathematics
Course
MATA30H3
Professor
Ken Butler
Semester
Winter

Description
Unit 1: Polynomial Functions  Polynomial Expression has the form: a n +a n-1a x +n-2+ a x + a x 3 a x+2a2 1 0  n: whole number  x: variable  a: coefficient X ER  Degree: the highest exponent on variable x, which is n. n  Leading Coefficient: a x n n  Power Functions: y = a*x , n EI  Even degree power functions may have line symmetry along y-axis.  Odd degree power functions may have point symmetry about origin.  Finite Differences: a ( n! )  Properties for Odd Functions:  Positive Leading Coefficients:  Goes from Q3 to Q1  Negative Leading Coefficients:  Goes from Q2 to Q4  Domain {XER} , Range {YER}  Properties for Even Functions:  Positive Leading Coefficients:  Goes from Q2 to Q1  Negative Leading Coefficients:  Goes from Q3 to Q4  Have local maximum/minimum points  Domain {XER}, Range above/beyond maximum/minimum points  Sketching Graphs  Sketch graphs according to its degree  Polynomial functions have 0 to maximum of n x-intercepts, where nis the degree.  Polynomial functions can also have at most n – 1 local max/mins, where n is the degree.  X – Intercepts are the roots of the function.  Factors of a factored form equation are also the roots.  Roots can have different orders, and are graphed differently:  Order 1 root [ie (x-1) ]  passes through the x-intercept  Order 2 root [ie x ]2  passes in tangent to the x-intercept 3  Order 3 root [ie x ]  passes through intercept like y = x at the origin  Even Function Test: f(-x) = f(x)  Odd Function Test: f(-x) = -f(x) n  Transformations of polynomial functions of the form y = a [ k (x-d) ] + c :  a >= 1 : vertical stretch by a factor of a.  0 <= a <= 1 : ve
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