Even and Odd Functions and Symmetry Types of

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Even and Odd Functions and Symmetry. Points and Symmetry. Types of Symmetry. Symmetry with respect to the. • x-axis. (x, y) & (x, -y) are reflections across the ...
Points and Symmetry

Even and Odd Functions and Symmetry

Types of Symmetry Symmetry with respect to the • x-axis (x, y) & (x, -y) are reflections across the x-axis • y-axis (x, y) & (-x, y) are reflections across the y-axis • Origin (x, y) & (-x, -y) are reflections across the origin

Determine if the given function is even, odd, or neither.

Even and Odd Functions • Even Function: graph is symmetric to the y-axis • Odd Function: graph is symmetric to the origin

In each case, replace x with –x and simplify. If the right side of the equation stays the same, the function is even. If every term on the right changes sign, then the function is odd.

• Note: Except for the function f(x) = 0, a function can not be both even and odd.

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Example

Example

Is this an even or odd function? What type of symmetry, if any does it have?

Example

Is this an even or odd function? What type of symmetry, if any does it have?

Is this an even or odd function? What type of symmetry, if any does it have?

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