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Polynomial functions are mathematical expressions that involve terms which are non-negative integer powers of the variable. These functions can have one or more terms, such as \(x^2\), \(3x^3\), or \(5x^0\). The general form of a polynomial function is:
\[ f(x) = a_n x^n + a_{n-1} x^{n-1} + ... + a_1 x + a_0 \] where \(a_n\) are constants and \(n\) is a non-negative integer.
Polynomials are known for their smooth and continuous graphs. A significant feature of polynomial functions is that they don't have breaks or holes. They can be added, subtracted, multiplied, and divided (except by a polynomial of a higher degree leading to a discontinuity).
Regardless of degree, every polynomial function is defined for all real numbers, meaning there are no restrictions on the input values.

A quadratic function is a type of polynomial function where the highest exponent of the variable is 2. The general form of a quadratic function is:
\[ f(x) = ax^2 + bx + c \] where \(a\), \(b\), and \(c\) are constants, with \(a \e 0\).
Quadratic functions describe a parabolic shape when graphed, either opening upwards or downwards, depending on the sign of \(a\). This

Interval notation is a way to represent subsets of real numbers. For example, the domain of a polynomial function like \( f(x) = x^2 - 2x + 3 \) is all real numbers, which in interval notation is written as: \[ (-\backslash infty, \backslash infty) \] Interval notation uses parentheses \(()\) to denote that an endpoint is not included, and brackets \[ [] \] to indicate an endpoint is included. For instance, the interval \( (2, 5] \) includes all real numbers greater than 2 and up to, and including, 5.