High School Math-Advanced Function-Polynomial Function
What is Polynomial Function ?
Polynomial Function is an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s). it can be express in a generic form as shown below.
How to Graph ?
You can graph any polynomial functions by both hands(harder method) and technology(easier method).
When graphing with hands, you need to know the x-intercepts(also known as roots), y-intercept, and end behaviours of the function. Some of the tips you can use for drawing by hands are
< Quadrant on a Cartesian Coordinate >
Descartes rule of signs
This rule is used to identify the number of positive roots, negative roots, and/or imaginary Roots of a polynomial function. By the application of this rule, you can identify whether you found the correct roots or not.
Even and odd functions
Odd function is an odd-degree function with a point symmetry, proved by f(-x)=-f(x), x can be any real numbers
Even function is an even-degree function with a line symmetry, proved by f(x) = f(-x), x can be any real numbers
< Synthetic Division >
Write the answer in P(x)Q(x)+R(x) format