Vocabulary
Polynomial- A monomial or a sum of monomials, each of which is called a term of the polynomial.
Polynomial Function- A function of the form f(x)=anxⁿ + an-1xⁿ⁻¹+...+a₁x + a₀ where an≠0, the exponents are all whole numbers, and the coefficients are all real numbers.
Synthetic Substitution- a method used to evaluate a polynomial function.
End Behavior-The behavior of the graph of a function as x approaches positive infinity (+∞) or negative infinity (-∞).
Polynomial Function- A function of the form f(x)=anxⁿ + an-1xⁿ⁻¹+...+a₁x + a₀ where an≠0, the exponents are all whole numbers, and the coefficients are all real numbers.
Synthetic Substitution- a method used to evaluate a polynomial function.
End Behavior-The behavior of the graph of a function as x approaches positive infinity (+∞) or negative infinity (-∞).
Essential Information
A monomial is a number, a variable, or a product of numbers and variables. A polynomial is a monomial or a sum of monomials. A polynomial function is a function of the form.
where an≠0, the exponents are all whole numbers, and the coefficients are all real numbers. For this function, an is the leading coefficient, n is the degree, and a₀ is the constant term. A polynomial function is in standard form if its terms are written in descending order of exponents from left to right.
Synthetic Substitution
Another way to evaluate a polynomial function is to use synthetic substitution. This method involves fewer operations than direct substitution.
Another way to evaluate a polynomial function is to use synthetic substitution. This method involves fewer operations than direct substitution.
End Behavior
The end behavior of a function's graph is the behavior of the graph as x approaches positive infinity (+∞) or negative infinity(−∞). For the graph of a polynomial function, the end behavior is determined by the function's degree and the sign of its leading coefficient.
The end behavior of a function's graph is the behavior of the graph as x approaches positive infinity (+∞) or negative infinity(−∞). For the graph of a polynomial function, the end behavior is determined by the function's degree and the sign of its leading coefficient.
Graphing Polynomial Functions
To graph a polynomial function, first plot points to determine the shape of the graph's middle portion. Then the information on end behavior to sketch the end behavior of the graph to sketch the ends of the graph.
To graph a polynomial function, first plot points to determine the shape of the graph's middle portion. Then the information on end behavior to sketch the end behavior of the graph to sketch the ends of the graph.