Characteristics of Polynomial Functions
Hmwk: pg 136#1-3, 4abcd, 5, 6ac, 7, 8, 10ab, 11, 13, (16)
Characteristics of Polynomial Functions
Polynomial functions have common features depending on the sign of the leading coefficient and the degree.
Leading Coefficient - the coefficient of the term with the highest degree in a polynomial; usually it is the first coefficient.
1. Examine the following functions and state their degree.
a) [pic] b) [pic]
degree = __ degree = __
c)[pic] d) [pic]
degree = __ degree = __
All of the functions above have an _____ degree.
Key Features of Odd Degree Functions
End behaviours
• If the leading coefficient is positive, then the function extends from the ______ quadrant to the _______ quadrant; ie as [pic],[pic] and as [pic],[pic].
• If the leading coefficient is negative, then the function extends from the ___ quadrant to ________ quadrant; ie as [pic],[pic] and as [pic],[pic].
Turning Points
• These polynomials will have at most "n - 1" turning points; notice in 'd)' that there are only ____ turning points even though the function is of degree ___.
Number of Zeroes (x-intercepts)
• They will have at least ____ x-intercept with a maximum of 'n' x-intercepts.
2. Examine the following functions and state their degree.
a) [pic] b) [pic]
degree = ___ degree = ___
c) [pic] d) [pic]
degree = ___ degree = ___
All of the functions above have an _____ degree.
Key Features of Even Degree Functions
End behaviours
• If the leading coefficient is positive, then the function extends from the ______ quadrant to the _______ quadrant; ie as [pic],[pic] and as [pic],[pic].
• If the leading coefficient is negative, then the function extends from the ___ quadrant to ________ quadrant; ie as [pic],[pic] and as [pic],[pic].
Turning Points
• These polynomials will have at most "n - 1" turning points.
Number of Zeroes (x-intercepts)
• They may not have any x-intercepts but can have a maximum of 'n' x-intercepts.
Symmetry of Polynomial Functions
Polynomial functions can have odd, even or no symmetry. If a polynomial does have symmetry, it tends to follow the degree. ie; If a quartic function (degree 4) has symmetry then it will be even since the degree is even, but not all quartics have symmetry.
***CAREFUL!! While the symmetry and degree of a function are similar, they are not necessarily the same concept. ***
Practice
|Degree | |
|Even or Odd Degree | |
|Sign of Leading | |
|Coefficient | |
|Max # of | |
|Turning Points | |
|Max # of | |
|x-ints | |
|End Behaviours | |
Given the followig functions, complete the tables below.
a) [pic] b) [pic] c)[pic]
|Degree | |
|Even or Odd Degree | |
|Sign of Leading | |
|Coefficient | |
|Max # of | |
|Turning Points | |
|Max # of | |
|x-ints | |
|End Behaviours | |
|Degree | |
|Even or Odd Degree | |
|Sign of Leading | |
|Coefficient | |
|Max # of | |
|Turning Points | |
|Max # of | |
|x-ints | |
|End Behaviours | |
-----------------------
[pic]
[pic]
[pic]
[pic]
[pic]
[pic]
[pic]
[pic]
................
................
In order to avoid copyright disputes, this page is only a partial summary.
To fulfill the demand for quickly locating and searching documents.
It is intelligent file search solution for home and business.
Related download
- list of positive behavior skills ten sigma
- strengths of character worksheet winona state
- identifying strengths interests abilities hopes and
- improving self esteem
- how to complete the worksheet
- the positive attitude development workbook
- acknowledging your positives
- positive qualities record cci
- positive character traits scholastic
- positive traits therapist aid
Related searches
- finding polynomial functions calculator
- zeros of polynomial functions
- how to find zeros of polynomial function
- zeros of polynomial functions calculator
- roots of polynomial factor form
- identifying polynomial functions calculator
- the functions and characteristics of money
- functions and characteristics of money
- roots of polynomial functions calculator
- rational zeros of polynomial calculator
- find zeros of polynomial function
- find roots of polynomial calculator