Aug 2, 2021 · We have seen the graphs of the basic reciprocal function and the squared reciprocal function from our review of toolkit functions. These graphs have several important features.

In fact, scientists and mathematicians frequently simplify complex mathematical models by substituting a polynomial model that is "close enough" for their purposes. In this section, we will study the graphs of …

Some are conceptually simple, such as the inverse relationship regarding pressure and volume, and others are more complex. While their formulas seem more straightforward than many you will …

These two functions are examples of power functions, functions that are some power of the variable. Where the base is a variable and the exponent, p, is a number. Which of our toolkit functions are …

A rational function is a function of the form R(z) = P(z) Q(z) where P and Q are polynomials. We can, and do, assume P and Q have no common factors, i.e., no common zeros.

Since a rational function represents division of two values that can be calculated for all real numbers (because they are represented through polynomials), the value of a rational function cannot be …

Understand polynomial and rational functions. Identify the degree, lead coefficient and constant term of a poly-nomial function from its equation. Given the graph of a polynomial function, determine its …

By combining root functions with polynomials, we can define general algebraic functions and distinguish them from the transcendental functions we examine later in this chapter.

Complex rational expressions can be simplified into equivalent expressions with a polynomial numerator and polynomial denominator. They are reduced to lowest terms if the numerator and denominator …

We have learned various techniques for factoring polynomials with up to four terms. The challenge is to identify the type of polynomial and then decide which method to apply.