Explain what makes a function a polynomial. Give an example of a function that is a polynomial and a function that is not a polynomial.
Given the polynomial f(x) = 2x3 + 5x2 - x - 5, answer the following questions:
Graph the polynomial. What is the degree of the polynomial?
Explain the constant in the polynomial and how it relates to the graph.
Define the x-intercepts of the polynomial.
Explain the relative maximum and relative minimum of the polynomial in the interval [-3,2]. Is there a different between the relative maximum and minimum and the absolute maximum and minimum?
What is a rational function? Give an example. For your example, answer or perform the following:
A function f(x) is a polynomial if it has the form
a_0 + a_1 x + a_2 x^2 + ... + a_n x^n
where a_0, a_1, a_2, .., a_n are numbers.
Given the polynomial f(x) = 2x^3 + 5x^2 - x - 5
and enter 2x^3 + 5x^2 - x - 5
in the box
(b) the polynomial has degree 3, because 3 is the largest exponent on x
(c) the number at ...
This provides examples of relating functions and polynomials and examples of working with a rational function.