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?

Any number which can be expressed in the form of a fraction p/q where p and q are integers and q is not equal to zero is called a rational number. Positive integers, negative integers ,zeros and common fractions belong to the system of rational numbers. P can be equal to zero.

A polynomial function is a function consisting of polynomials. A polynomial is an algebraic expression consisting of one or more terms in each of which the exponent of the variable is zero or positive integer. Thus 2,3x, x²+ 3x-4 etc are polynomials.

A polynomial consisting of a single term is monomial e.g, 2, 3x , xy

A polynomial consisting of two terms is binomial e.g, 2+3x , xy- 5z etc.

A polynomial consisting of three terms is trinomial e.g, 2+3x +xy

Terms containing the same variable and same corresponding exponents are known as like terms.

Terms having different variables or same variable but different exponents are called unlike terms.

Polynomials are used to sketch curves or daily life problems.

To sketch the graphs first we find the intercepts, then the vertical asymptotes and the horizontal asymptote, by solving.

The vertical asymptotes divide the number line into regions after which the graph is sketched.

The first thing that comes to the mind is the form of p/q for rational functions and algebraic expressions for the polynomial functions.

psm22415 psm22415 · Answer 2 · 2021-12-09T02:25:42+01:00

The fundamental difference between the graphs of the polynomial function and rational function is that the graph of the polynomial function is continuous in nature while the graph of the rational function is discontinuous in nature as the denominator will be zero at some point.

The strategy are using to get graph of polynomial and rational function given below.

Polynomial is an expression comprising variables and coefficients.

The rational expression is fractions involving polynomials

Polynomial: A 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 : A 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: The definition of rational is something that makes sense or that could be based in fact or someone who behaves and thinks logically.

Rational Function: A 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 given below.

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

The fundamental difference between the graphs of the polynomial function and rational function is that the graph of the polynomial function is continuous in nature while the graph of the rational function is discontinuous in nature as the denominator will be zero at some point.

To know more about Graph click the link given below.

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