1.2 Even Odd Functions

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What is an even function?

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A function f(x) is called an even function if for every x in the domain, f(-x) = f(x). Example: f(x) = x^2.

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CCSS.HSF.BF.B.3

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What is an odd function?

Back

A function f(x) is called an odd function if for every x in the domain, f(-x) = -f(x). Example: f(x) = x^3.

Tags

CCSS.HSF.BF.B.3

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What does it mean if a function is neither even nor odd?

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A function is neither even nor odd if it does not satisfy the conditions for being even or odd. Example: f(x) = x^2 + x.

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CCSS.HSF.BF.B.3

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Back

Neither.

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CCSS.HSF.BF.B.3

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Back

Odd.

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CCSS.HSF.BF.B.3

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What is the graphical representation of an even function?

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An even function is symmetric about the y-axis.

Tags

CCSS.HSF.BF.B.3

Front

What is the graphical representation of an odd function?

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An odd function is symmetric about the origin.

Tags

CCSS.HSF.BF.B.3

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If f(x) = 2x^4 - 3x^2 + 1, is it even, odd, or neither?

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Even.

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CCSS.HSF.BF.B.3

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If f(x) = x^5 - 4x, is it even, odd, or neither?

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Odd.

Tags

CCSS.HSF.BF.B.3

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What is the test for determining if a function is even?

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Check if f(-x) = f(x) for all x in the domain.

Tags

CCSS.HSF.BF.B.3