Answer to Question #148284 in Algebra for Duhamel

Question

Reflect on the concept of polynomial and rational functions. What concepts (only the names) did you need to accommodate these concepts in your mind? What are the simplest polynomial and rational function you can imagine? In your day to day, is there any occurring fact that can be interpreted as polynomial and rational functions? What strategy are you using to get the graph of polynomial and rational functions?

Answer 1

Polynomial is an expression comprising variables and coefficients.

The rational expression is fractions involving polynomials

Polynomial: is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.

An example of a polynomial of a single indeterminate, x, is x² − 4x + 7

Polynomial Function : is a function which involves only non-negative integer powers or only positive integer exponents of a variable in an equation like the quadratic equation, cubic equation

Rational: is something that makes sense or that could be based in fact or someone who behaves and thinks logically.

Rational Function: is any function which can be defined by a rational fraction, i.e. an algebraic fraction such that both the numerator and the denominator are polynomials. The coefficients of the polynomials need not be rational numbers; they may be taken in any field K.

polynomials are used to describe curves of various types, people use them in the real world to graph curves. For example, roller coaster designers may use polynomials to describe the curves in their rides.

Process for Graphing a Rational Function and Polynomials

1. Find the intercepts, if there are any
2. Find the vertical asymptotes by setting the denominator equal to zero and solving.
3. Find the horizontal asymptote, if it exists, using the fact above
4. The vertical asymptotes will divide the number line into regions
5. Sketch the graph.