![]() ![]() Even functions are symmetric about the y axis, odd functions are symmetric about the origin. Even functions: opposite inputs have the same input. So remember odd functions: opposite inputs have opposite outputs. Now some examples from our parent functions are y=x, y equals x cubed and also y equals 1 over x. After the point of reflection in origin, the pre-image ABC is transformed into A’B’C’. Let ABC be the triangle, and the coordinates are A(1,4), B(1,1), and C(5,1). So it's 180 degrees symmetry about the origin. Reflection in origin (0, 0) In the coordinate plane, we can use any point as the point of reflection. ![]() That means is you could take the the graph, rotate it 180 degrees and it will look exactly the same. Now, if this is true, the graph of an odd function would be symmetrical with respect to the origin. This means that opposite inputs give opposite outputs. Function f is odd if f of -x equals the opposite of f of x. There's y=x squared and there's y equals the absolute value of x. Now let's look at two examples from our parent functions. y equals f of -x is a reflection about the y axis, if the reflection of about the y axis of a function is exactly same the same as the function itself then it's symmetric about the y axis. ![]() Well, if you remember our discussion of symmetry, of reflections, the graph of y equals f of -x. Now what kind of symmetry does that give us? Well the graph of an even function's always going to be symmetric with respect to y axis. That means that you can switch x for -x and get the same value. A function f is even if f of -x equals f of x for all x in the domain of f. I want to talk about even and odd functions. ![]()
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