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How to Determine If a Function Is Even or Odd

A: Symmetry Test |
B: Graphical Analysis |
C: Algebraic Test |
D: Differentiation Test

User Riina
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Final answer:

To determine if a function is even or odd, an Algebraic Test can be used, checking if y(x) = y(-x) for even functions or y(x) = -y(-x) for odd functions. Graphical Analysis also helps by checking symmetry around the y-axis for even functions or point reflection at the origin for odd functions.

Step-by-step explanation:

To determine if a function is even or odd, you can use the Algebraic Test. An even function satisfies the condition y(x) = y(-x), meaning it is symmetric about the y-axis. For example, the function x² is even because (x²) = (-x)². On the other hand, an odd function meets the condition y(x) = −y(-x), indicating that it has rotational symmetry about the origin. A common example of an odd function is x³, as (x³) = −(-x)³. You can also observe symmetry by conducting a Graphical Analysis of the function's plot; even functions will reflect over the y-axis, while odd functions will exhibit a point reflection at the origin. However, the Differentiation Test is not typically used to determine even or odd functions.

User Daqs
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