Class Notes (835,072)
Canada (508,911)
Mathematics (856)
MATA30H3 (41)
Lecture

unit 1 to 2.docx

4 Pages
92 Views
Unlock Document

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
More Less

Related notes for MATA30H3

Log In


OR

Join OneClass

Access over 10 million pages of study
documents for 1.3 million courses.

Sign up

Join to view


OR

By registering, I agree to the Terms and Privacy Policies
Already have an account?
Just a few more details

So we can recommend you notes for your school.

Reset Password

Please enter below the email address you registered with and we will send you a link to reset your password.

Add your courses

Get notes from the top students in your class.


Submit