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Course: Algebra 2 > Unit 9
- Function symmetry introduction
- Even and odd functions: Graphs
- Even and odd functions: Tables
- Even and odd functions: Graphs and tables
- Even and odd functions: Equations
- Even and odd functions: Find the mistake
- Even & odd functions: Equations
Symmetry of polynomials
What you should be familiar with before taking this lesson, what you will learn in this lesson, investigation: symmetry of monomials.
- If f ( − x ) is the same as f ( x ) , then we know f is even.
- If f ( − x ) is the opposite of f ( x ) , then we know f is odd.
- Otherwise, it is neither even nor odd.
f ( − x ) = 4 ( − x ) 3 = 4 ( − x 3 ) ( − x ) 3 = − x 3 = − 4 x 3 Simplify = − f ( x ) Since f ( x ) = 4 x 3
- (Choice A) Even A Even
- (Choice B) Odd B Odd
- (Choice C) Neither even nor odd C Neither even nor odd
Concluding the investigation
Investigation: symmetry of polynomials, example 1: f ( x ) = 2 x 4 − 3 x 2 − 5 , example 2: g ( x ) = 5 x 7 − 3 x 3 + x , example 3: h ( x ) = 2 x 4 − 7 x 3 , check your understanding, want to join the conversation.
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