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?
Part II:
What is a rational function? Give an example. For your example, answer or perform the following:
Graph the rational function.
Give the domain and range of the rational function.
Find the vertical and horizontal asymptotes of the rational function.
Solution Preview
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
(a) visit
http://www.walterzorn.com/grapher/grapher_e.htm
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 the ...
Solution Summary
The provides examples of relating functions and polynomials and examples of working with a rational function.
To understand Polynomials and rational functions - To explore the versatility of rational functions, choose a second-order/third-order (eg, x2/x3) and a third ...
Mathematics - Polynomial & Rational Functions. Exercise 4.1 29. ... The Solution file is attached. The polynomial and rational functions are examined. ...
One of the advantages of rational functions is that even rational functions with low-order polynomials can provide excellent fits to complex experimental data. ...
... This becomes a linear function (of degree 1). A rational function is formed when one polynomial function is divided by another polynomial function. ...
