1-2 Day Two Even/Odd Functions

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Presentation transcript:

1-2 Day Two Even/Odd Functions

Symmetry y-axis if (x,y) is on the graph, so is (-x,y) x-axis Origin if (x, y) is on the graph, so is (-x, -y) give an example

Even/Odd Functions A function with y-axis symmetry is considered EVEN. (Can you guess why?) A function with symmetry about the origin is considered ODD. (Why?) A function cannot have x-axis symmetry. (Why?)

Odd or even? y = x2 + 4 y = x2 + 2x + 1 y = x3 – 4x y = x3 – 1 Use the graph and specific points to convince yourself. Then prove algebraically. Can a function be both even and odd? Neither? Do you see any patterns/shortcuts?