To determine: The argument that shows that every polynomial family of degree
It is not possible to get all the polynomials in the family by simple transformations.
Given Information:
The parent function is
Explanation:
Consider the given function,
A polynomial function of degree n can have at most n- 1n -1 turning points. A polynomial of degree more than 2 will have more than 1 turning points.
This implies there is more than one shape possible for a polynomial of degree n , when
The graph of
Therefore, for
There are two types of polynomials of degree 3, Some have 2 turning points, some of 0 turning points. By simple transformations from
It is not possible to get the cubic polynomials which have two turning points from the transformation of
Therefore, it is not possible to get all the polynomials in the family by simple transformations.
Chapter 5 Solutions
High School Math 2015 Common Core Algebra 2 Student Edition Grades 10/11
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