Sect+1-7+Guided+Notes+-+Student

Sect+1-7+Guided+Notes+-+Student - 2 4 2 4 ) ( x x x f-= A...

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Math 1111-11. Guided Notes. Sections 1.7. Symmetry Symmetry with respect to the y-axis : For every point (x, y) on the graph, (-x, y) is also on the graph. Test: Substitute –x for x. If an equivalent equation results, the graph of the equation is symmetric with respect to the y-axis. 2 x y = Symmetry with respect to the x-axis : For every point (x, y) on the graph, (x, -y) is also on the graph. Test: Substitute –y for y. If an equivalent equation results, the graph of the equation is symmetric with respect to the x-axis. 3 2 - = y x Symmetry with respect to the origin : For every point (x, y) on the graph, (-x, -y) is also on the graph. Test: Substitute –x for x and –y for y. If an equivalent equation results, the graph of the equation is symmetric with respect to the origin. 3 x y =

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Even and Odd Functions A function f is even if, for all x in the domain of f , ). ( ) ( x f x f = - In other words, functions whose graphs are symmetric with respect to the y-axis are even functions . Example:
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Unformatted text preview: 2 4 2 4 ) ( x x x f-= A function f is odd if, for all x in the domain of f , ). ( ) ( x f x f-=-In other words, functions whose graphs are symmetric with respect to the origin are odd functions . Example: x x x f 3 ) ( 3-= A function f is neither even nor odd if it does not satisfy the conditions for either. Example: x x x f 2 ) ( 2 + = Symmetry Additional Examples Ex 1. Draw something that shows each of these symmetries. Symmetry with respect Symmetry with respect Symmetry with respect to the x-axis to the y-axis to the origin Ex 2. Find the point that is symmetric to (-3,2) with respect to the x-axis, y-axis, and origin. Ex 3. Test algebraically whether 2 4 3 2 y x = + is symmetric with respect to the x-axis, y-axis, and origin. Even and Odd Functions Ex 4. Determine if the following functions are even, odd, or neither. A. 4 ) ( 2 +-= x x f B. x x x x f 2 6 5 ) ( 3 7--= C. 7 3 5 ) ( 2 6--= x x x h...
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This note was uploaded on 08/14/2008 for the course MATH 1111 taught by Professor Teachey during the Summer '08 term at Kennesaw.

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Sect+1-7+Guided+Notes+-+Student - 2 4 2 4 ) ( x x x f-= A...

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