Even and Odd Functions (Algebraically)
A function is classified as an even or odd function based on the symmetry of its graph, but it can also be determined to be even, odd, or neither using Algebra. In this video I will show you how a function is odd if substituting -x in a function results in -f(x), even if substituting -x in the function results in the original function, and neither if substituting -x results in neither the original function nor the -f(x). This Algebraic method will show whether any function is even, odd, or neither.
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Video highlights:
00:00 Introduction
00:14 Algebraic definition of an even or odd function
00:35 f(x)=x^5+2^x3−x example of determining an odd function Algebraically
02:42 f(x)=x^4+3x^2−2 example of determining an even function Algebraically
04:01 f(x)=2x^3−x^2+x example of determining that a function is neither even nor odd
06:30 Conclusion