Warm Up Find the following: (f + g)(-1) = (g f)(x) = (g - f)(2) = (f /g)(x) =

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Warm Up Find the following: (f + g)(-1) = (g f)(x) = (g - f)(2) = (f /g)(x) =

Even & Odd Functions March 6 th, 2014

What are even & odd functions? Plug in 3 to this equation… Now plug in -3… What do you notice about the answers?

What are even & odd functions? Plug in 3 to this equation… Now plug in -3… What do you notice about the answers?

What are even & odd functions? Plug in 3 to this equation… Now plug in -3… What do you notice about the answers?

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:

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:

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:

Even Functions-Graphing

Even Functions Graphing Determine which are even…

Odd Functions-Graphing

Odd Functions Graphing Determine which are odd…

Even Functions-Algebraically Plug in –x and simplify! If you get the same function, it is even!

Odd Functions-Algebraically Plug in –x and simplify! If you get the opposite function, it is odd!

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! 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! Still -5

Example:

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

Example: Determine if the function is even, odd, or neither.

Example: Determine if the function is even, odd, or neither.

Example: Determine if the function is even, odd, or neither.

Example: Determine if the function is even, odd, or neither.

Example: Determine if the function is even, odd, or neither.

Example: Determine if the function is even, odd, or neither.

Example: Determine if the function is even, odd, or neither.

NC Final Exam Question Example Which of the following is an even function?

Challenge Question Is (x+1) 2 even, odd, or neither?

Challenge Question Can a function be both even and odd?

Classwork Complete side 1 of the worksheet the graphs #1-11, and #12-19

Homework Complete the back side of the worksheet! Graphs & multiple choice questions from