Reflection: Developing a Conceptual Understanding Analyzing Polynomial Functions - Section 1: Introduction


Students easily confuse the difference between an odd and even function, and an odd-degree and even-degree function.  I start by asking students four questions while looking at a set of graphs. The

1.  Which are odd functions?

2.  Which are even functions?

3.  Which graphs are symmetric about the y-axis?

4.  Which graphs are symmetric about the origin?

Most of the students skip over questions one and two for lack of understanding.  Some students identify which are functions, not understanding the meaning of an odd and even function.

Students then move on to symmetrical about the y-axis and most of the students have some understanding of this.

Then, I have students look at the set of graphs and determine which ones are symmetrical about the origin.  Some students struggled with this, but other students recognized that if the graph is rotated 180 degrees about the origin, it would land on the same graph.  

This helped the other students visualize it when students shared out.  I also demonstrated with rotating the image on a piece of paper two 90 degree turns.

As students are sharing out about this activity, I first have them share responses for number three and four.  Then I provide the definition of odd function and even function, and then students realize that they are the same answers in one and two as three and four.  Even functions are the same graphs that are symmetric about the y-axis, and Odd functions are the same as symmetric about the origin.  

I do not have students prove it algebraically at this time, only by viewing the graph.

  Developing Odd and Even Functions from students' prior knowledge of symmetry
  Developing a Conceptual Understanding: Developing Odd and Even Functions from students' prior knowledge of symmetry
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Analyzing Polynomial Functions

Unit 8: Quadratic Functions
Lesson 10 of 10

Objective: SWBAT identify the degree of a Polynomial, the sign of the leading coefficient, the intercepts, the multiplicity of the zeros, and the end behavior to determine the shape of the graph.

Big Idea: To be able to sketch an approximate graph of a Polynomial function from key characteristics without a calculator.

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analyzing polynomioals
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