![]() ![]() Remember that the domain of any polynomial function is the set of all real numbers. We can represent all the polynomial functions in the form of a graph. We just need to take care of the exponents of variables to determine whether it is a polynomial function. Note: Remember that coefficients can be fractions, negative numbers, 0, or positive numbers. The below-given table shows an example and some non-examples of polynomial functions: Functions The variable should not be in the denominator.The variable of the function should not be inside a radical i.e, it should not contain any square roots, cube roots, etc.I.e., the exponent of the variable should not be a fraction or negative number. ![]() The exponent of the variable in the function in every term must only be a non-negative whole number.In order to determine if a function is polynomial or not, the function needs to be checked against certain conditions for the exponents of the variables. Some examples of a cubic polynomial function are f(y) = 4y 3, f(y) = 15y 3 – y 2 + 10, and f(a) = 3a + a 3. It is of the form f(x) = ax 3 + bx 2 + cx + d. Cubic Polynomial FunctionĪ cubic polynomial function has a degree 3. Some examples of a quadratic polynomial function are f(m) = 5m 2 – 12m + 4, f(x) = 14x 2 – 6, and f(x) = x 2 + 4x. ![]() Quadratic Polynomial FunctionĪ quadratic polynomial function has a degree 2. Some examples of a linear polynomial function are f(x) = x + 3, f(x) = 25x + 4, and f(y) = 8y – 3. Linear Polynomial FunctionĪ linear polynomial function has a degree 1. Since f(x) = a constant here, it is a constant function. Zero Polynomial FunctionĪ zero polynomial function is of the form f(x) = 0, yes, it just contains just 0 and no other term or variable. The four most common types of polynomials that are used in precalculus and algebra are zero polynomial function, linear polynomial function, quadratic polynomial function, and cubic polynomial function. Examples: x 3 – 3 + 5x, z 4 + 45 + 3z, and x 2 – 12x + 15įurther, the polynomials are also classified based on their degrees.
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