Math Tutoring on Determining Odd and Even Functions
There are two main ways to determine if a function is even or odd. One is an Algebraic method, and the other is a Graphical method. A function is even if algebraically f of x = f of -x, and graphically the graph has symmetry across the y axis. If we are working with a polynomial function, a polynomial function will have all even exponents on the variables. For odd functions algebraically, -f of x = f of x, and graphically the graph has rotational symmetry about the origin, which means the graph remains the same after a rotation of 180. A polynomial function that is odd will have all odd exponents on the variable. Following steps are followed in math tutoring:
To reflect the point about the x axis, replace y with -y.
To reflect the point about the y axis, replace x with -x.
To reflect a point about the origin, replace x with -x and y with –y.
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1. How can you determine whether a function is even or odd?
2. What is the Algebraic method to find a function to be odd or even?
3. What is the Graphical method to find a function to be odd or even?
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