Linear, quadratic, and cubic functions are members of the family of polynomial functions. A polynomial function of degree n is given by Ę(x) = anxn + anā1xnā1 +ā¦+ a1x + a0, where n is a whole number and an, anā1, ā¦, a1, a0 are real numbers with an ā 0.
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Consider the key components of this definition to clarify their meanings.
Polynomial function of degree n means that the degree of a polynomial is shown in the definition by n. The degree is the highest exponent of any term in the polynomial.
Where n is a whole number means that the highest exponent, n, of a polynomial function must be a whole number. It cannot be a fraction, decimal, or negative value. This means that all other exponents in the function must be whole numbers.
an, anā1, ā¦, a1, a0 are real numbers means that, in the function, every coefficient and the constant term, a0, must be real numbers.
an ā 0 means the leading coefficient, an, cannot be 0. If the leading coefficient is 0, then the leading term is 0, which changes the degree of the polynomial.
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Complete the questions on page 287 (1a, 1b, 1c, and 1d) for practice in identifying key features of a polynomial function. Click here to verify your answers.
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