A polynomial function is a function that can be expressed as a sum of terms, each consisting of a constant coefficient multiplied by a variable raised to a non-negative integer power. For example, q(x) = 3x^4 - 5x^3 - 2x^2 + x - 18 is a polynomial function of degree 4, because the highest power of x is 41
Some of the properties and features of polynomial functions are:
The domain of a polynomial function is the set of all real numbers, meaning that the function is defined for any value of x.
The range of a polynomial function is the set of all possible outputs or y-values that the function can produce.
The end behavior of a polynomial function describes how the function behaves as x approaches positive or negative infinity. The end behavior depends on the degree and the leading coefficient of the polynomial function.
The zeros or roots of a polynomial function are the values of x that make the function equal to zero. The zeros can be found by factoring the polynomial or using other methods such as synthetic division or the rational root theorem.
The graph of a polynomial function is a smooth and continuous curve that may have one or more turning points, where the function changes direction. The turning points correspond to the local maximums or minimums of the function.
The multiplicity of a zero of a polynomial function is the number of times that the zero occurs as a factor in the factored form of the polynomial. The multiplicity affects how the graph crosses or touches the x-axis at that zero.