What are Odd Functions? | Functions and Relations, Function Symmetry, Even and Odd Functions скачать в хорошем качестве

What are Odd Functions? | Functions and Relations, Function Symmetry, Even and Odd Functions

What is an odd function? Odd functions, like even functions, have a special type of symmetry. The graph of an odd function has rotational symmetry about the origin. So, if we rotate the graph of an odd function 180 degrees about the origin, it will appear as though we haven't rotated it at all! It's pretty neat, and we go into further detail in the full video lesson, including the definition of an odd function, and how to show that a function is odd! In order for a function to be odd, every element of its domain must satisfy the equation f(-x) = - f(x). If this is the case, the function is odd! My lesson on even functions:    • What are Even Functions? | Functions and R...   SOLUTIONS TO PRACTICE PROBLEMS: 1. f(x) = x^5 - x^2 f(-x) = (-x)^5 - (-x)^2 = (-x)^5 - x^2 -f(x) = -x^5 + x^2 Thus, f(-x) is not equal to -f(x), so f is not odd. 2. g(x) = x^3 + 3x g(-x) = (-x)^3 - 3x = (-x)^3 - 3x -g(x) = -(x^3) - 3x = (-x)^3 - 3x Thus, g(-x) = -g(x), so g is odd. I hope you find this video helpful, and be sure to ask any questions down in the comments! ******************************************************************** The outro music is by a favorite musician of mine named Vallow, who, upon my request, kindly gave me permission to use his music in my outros. I usually put my own music in the outros, but I love Vallow's music, and wanted to share it with those of you watching. Please check out all of his wonderful work. Vallow Bandcamp: https://vallow.bandcamp.com/ Vallow Spotify: https://open.spotify.com/artist/0fRtu... Vallow SoundCloud:   / benwatts-3   ******************************************************************** +WRATH OF MATH+ ◆ Support Wrath of Math on Patreon:   / wrathofmathlessons   Follow Wrath of Math on... ● Instagram:   / wrathofmathedu   ● Facebook:   / wrathofmath   ● Twitter:   / wrathofmathedu   My Music Channel:    / seanemusic