Even and odd functions

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  1. What are even and odd functions?
    • How to determine if it is an even or odd function graphically and algebraically?
  1. Determine if the function f(x)=7x9+12f(x)=7x^9+12 is even, odd, or neither
    1. Determine if the function f(x)=3x7+4x590x2f(x)=3x^7+4x^5-90x^2 is even, odd, or neither
      1. Determine if the function f(x)=400xsin(x) f(x)=400xsin(x) is even, odd, or neither
        1. Determine if the function y=4x8+2x47x2y=4x^8+2x^4-7x^2 is even, odd, or neither
          1. Determine if the function y=7csc(x)+2tanxy=7csc(x)+2tanx is even, odd, or neither
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            Topic Notes
            If we are asked whether a given graph is symmetrical about the y-axis or not, it's easy to answer because we only need to see if there is a mirror image about the y-axis or not. But what if we are only given a function, but not the graph? In this section, we will broaden our knowledge about symmetry in functions while classifying symmetries algebraically, as well as learning the notion of odd and even functions.
            When f(x)=f(x),f(-x) = f(x), function is even
            f(x)=f(x),f(-x) = -f(x), function is odd