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Published byBryce Sherman Modified over 5 years ago
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Do Now Find the following: (f + g)(-1) = (g ͦ f)(x) = (g - f)(2) = (f /g)(x) =
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Even & Odd Functions
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What are even & odd functions?
Plug in 3 to this equation… Now plug in -3… What do you notice about the answers?
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What are even & odd functions?
Plug in 3 to this equation… Now plug in -3… What do you notice about the answers?
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What are even & odd functions?
Plug in 3 to this equation… Now plug in -3… What do you notice about the answers?
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Even Functions A function is even when it is symmetric about the y-axis. Meaning when you plug in –x the function simplifies to be the same f(-x) = f(x) Examples:
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Odd Functions A function is odd when it is symmetric about the origin - the point (0,0) Meaning when you plug in –x & simplify the signs of each term changes! f(-x) = - f(x) Examples:
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Functions that are NEITHER
A function is neither when it is NOT symmetric about the y-axis or the origin Most functions are neither even nor odd Meaning when you plug in –x you get a completely different function that is not the same & does not have all signs changed Examples:
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So Basically… Plug in a negative and get Same # Different Signs Odd
Plug in a negative and get a Same Number Same Sign Even
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Even Functions-Graphing
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Even Functions Graphing Determine which are even…
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Odd Functions-Graphing
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Odd Functions Graphing Determine which are odd…
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Even Functions-Algebraically
Plug in –x and simplify! If you get the same function, it is even! Note: If the function has all EVEN exponents and/or a constant (#) it will be even! That means it has variable exponents of 2,4,6,etc…
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Odd Functions-Algebraically
Plug in –x and simplify! If you get the opposite function, it is odd! Note: If the function has all ODD exponents & NO constant it will be odd! That means EVERY variable term has an exponent of 1,3,5,7,etc…
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Neither Functions-Algebraically
Plug in –x and simplify! If you do not get the same function, or all of the signs do not change, it is neither! Still -5 If the function has a mixture of even or odd exponents, or odd exponents & a constant then it will be neither! This is the MOST COMMON!
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Example:
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Example:
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Example:
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Example:
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Example:
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Example: Determine if the function is even, odd, or neither.
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Example: Determine if the function is even, odd, or neither.
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Example: Determine if the function is even, odd, or neither.
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Example: Determine if the function is even, odd, or neither.
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Example: Determine if the function is even, odd, or neither.
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Example: Determine if the function is even, odd, or neither.
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Example: Determine if the function is even, odd, or neither.
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Example: Determine if the function is even, odd, or neither.
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NC Final Exam Question Example
Which of the following is an even function?
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Challenge Question Is (x+1)2 even, odd, or neither?
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Challenge Question Can a function be both even and odd?
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Homework Worksheet front and back! Don’t forget to Justify!!!
Graphs & multiple choice questions from
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