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?

The Learning Journal entry should be a minimum of 400 words and not more than 750 words.

Answer 1

Solution:-

Given that

Polynomial Function:-

all functions of the form ax+b, , etc are called polynomial functions.

A function P(x) defined for all real values of x in the domain of P and given by the relation

where and n is a positive integer, is called a polynomial function of degree n and are called coefficients.

A polynomial function of 1st degree, ax+b is called a linear function and

a polynomial function of 2nd degree, is called a quadratic function.

Rational functions:-

A function f(x) defined by where P(x) and Q(x) are polynomial functions (where for any value of x in the domain of function) is called rational function.

are examples of rational functions.

Q2.

we need some concept to accomodate these functions

(1) knowledge of numbers real numbers, integers, complex numbers.

(2), sets:- Defination of sets, some examples

(3) Relation:- Defination of Relation, some examples and type of relations.

(4) Defination of Function, Domain, Range.

Q3

Simplest polynomial functions are

(1) f(x) = 1 (constant function is also a polynomial function of degree 0).

(2) f(x) = x

(3)

(4)

simplest rational functions are

(1)

(2)

(3)

(4)

Q4:-

(1) y = f(x) where x denote the time and y denote the speed. so our function tells us the speed at time t. this is a polynomial function. this fact can be interpreted as polynomial function.

(2) Suppose a person riding bike and distance cover by bike at time t can be interpreted by polynomial function.

(3) To represent cast in economics and to analyze and interpret data and draw conclusions in financial planning. this type of problems can be interpreted by polynomial functions.

(4) , this is hypothetical rational function representing the concentration of a drug in the patients blood stream with respect to time.

Q5

To draw the graph of polynomial and rational functions we need knowledge of some topics, that topics are

(1) roots of polynomial

(2) zeros of functions

(3) Derivative (Differentiation of functions)

(4) Incresing and decreasing functions.

for eg:-

f(x) = x

f'(x) = 1 is greater than 0

function is increasing and f(0) = 0

function pass through x = 0.

(2)

function is decreasing and function has no zeros mean graph of this function never cut x-axis

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