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

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

What is an even function? Even functions are functions with a special type of reflective symmetry. The graph of an even function is symmetric with respect to the y axis. So the y axis is like a mirror with even functions, on one side you have the image, and on the other you have the mirror image. It's pretty neat, and we go over the definition of even functions, plus examples in today's math video lesson! Since even functions are symmetric with respect to the y axis, you might be able to guess what the definition. The function's value on one side of the y axis must mirror the value on the other side. Thus, a function f is even if and only if f(x) = f(-x) for all elements x in the domain of the function. We go over several even function examples in the video, and discuss why even functions are called even functions. Examples include x^2, |x|, and 1-x^6. SOLUTIONS TO PRACTICE PROBLEMS: 1. f(x) = 2x - x^2 f(-x) = 2(-x) - (-x)^2 = -2x - x^2 Since -2x - x^2 is not equal to 2x - x^2, we know f(-x) is not equal to f(x), therefore f is not even. 2. g(x) = 3x^2 - x^4 g(-x) = 3(-x)^2 - (-x)^4 = 3x^2 - x^4 = g(x) Since g(x) = g(-x), g is even. 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