Rational Functions: Representing Real-life Situations and Solving Equations, Study notes of Earth science

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RATIONAL

FUNCTIONS

RATIONAL

FUNCTIONS

4.1 : Representing Real

life Situations using Rational

Functions

RATIONAL

FUNCTIONS

RATIONAL

FUNCTIONS

Functions are used to model real life

situations and in representing real

- life situations the quantity of one

variable depends or corresponds to

or mapped onto another quantity.

RATIONAL FUNCTIONSRATIONAL FUNCTIONS

Here are the examples of polynomial

functions of particular degree together with

their names:

Polynomial Degree Special Name 𝑓( 𝑥) = 3 0 Constant Function 𝑓( 𝑥) = −2𝑥 + 1 1 Linear Function 𝑓( 𝑥) = 3 𝑥 2 − 5 𝑥 + 2 2 Quadratic Function 𝑓( 𝑥) = 4 𝑥^3 + 2 𝑥 − 7 3 Cubic Function

RATIONAL FUNCTIONSRATIONAL FUNCTIONS DEFINITION OF RATIONAL FUNCTIONS A rational function, r(x) is a function of the form 𝑟(𝑥)= Where p(x) and q(x) are polynomial functions and (𝑥)≠ The domain of r(x) is a set of real numbers such that q(x) is not zero.

DEFINITION OF RATIONAL FUNCTIONS

A rational function, r(x) is a function of the form 𝑟(𝑥)= Where p(x) and q(x) are polynomial functions and (𝑥)≠ The domain of r(x) is a set of real numbers such that q(x) is not zero.

RATIONAL FUNCTIONSRATIONAL FUNCTIONS There are different scenarios or real-world relationships that can be modeled by rational functions, let us take the following examples

1. The Local Government Unit allotted a budget of ₱100,000.00 for the feeding program in the Day Care Center. The amount will be divided equally to all the pupils in the Day Care Center. Write an equation showing the relationship of the allotted amount per pupil represented by f(x) versus the total number of children represented by x

RATIONAL FUNCTIONSRATIONAL FUNCTIONS

1. The Local Government Unit allotted a budget of ₱100,000.00 for the feeding program in the Day Care Center. The amount will be divided equally to all the pupils in the Day Care Center. Write an equation showing the relationship of the allotted amount per pupil represented by f(x) versus the total number of children represented by x No. of children (x) 10 20 50 100 200 Allocated amount per child ₱10,000 ₱ 5000 ₱ 2000 ₱ 1000 ₱ 500 Notice that as the number of children increase the amount allocated per child decrease. In writing a representation we will arrived at 𝑓(x)=

RATIONAL FUNCTIONSRATIONAL FUNCTIONS

3. The Local Brgy received a budget of ₱200,000.00 to provide medical check-ups for the children in the Brgy. The amount is to be allotted equally among all the children in the Brgy. Write an equation f(x) representing the allotted amount per child(y-variable) versus the total number of children (x- variable). No. of children (x) 10 20 50 100 200 Allocated amount per child ₱20,000 ₱ 1000 ₱ 4000 ₱ 2000 ₱ 1000

Thus the representation of

F(x) =

RATIONAL FUNCTIONSRATIONAL FUNCTIONS

4. A Philanthropist wants to supplement the budget allotted for each child by providing an additional P 750 .00 for each in the Brgy. If g(x) represent the new allotted for each child, construct a function representing this relationshipNo. of children (x) 10 20 50 100 200 Allocated amount per child ₱20,000+ 750. ₱ 1000 + 750. ₱ 4000 + 750. ₱ 2000 + 750. ₱ 1000 + 750.

Thus the representation of

g(x) =+

Practice ExercisePractice Exercise

1. Let c(t)= +6 be the function that describes the concentration of a certain medication in the bloodstream overtime t. If 4 hours have passed after the medicine was intake, how concentrated is it in the blood? a. What is the rational function that serves as the model? b. How are you going to determine the concentration of the medicine given the rational function and the number of hours?

Practice ExercisePractice Exercise

1. Let c(t)= be the function that describes the concentration of a certain medication in the bloodstream overtime t. If 4 hours have passed after the medicine was intake, how concentrated is it in the blood? a. What is the rational function that serves as the model? ANSWER: c(t)=

Practice ExercisePractice Exercise

2. The distance between the school and your home is 5 kilometers. Express velocity ( v) as a function of travel time (t) in hours. ANSWER: V(t)=

Practice ExercisePractice Exercise

3. Suppose that c(t)= (in mg/ml) represent the concentration of a drug in a patient’s bloodstream t hours after the drug was administered. Construct a table of values for c(t) for t= 0,1,2, 5, t 0 1 2 5 10 concentration of a drug in a patient’s bloodstream 0 2.5 2 0.96 0.

Practice ExercisePractice Exercise

4. The distance from manila to baguio is around 250 kilometers. a. How long will take you to get to the baguio if your average speed is 25 kilometers per hours?40km/hrs?50km/hrs? 250km/25km/hrs= 10 hours 250km/40km/hrs= 6.25 hours 250km/50km/hrs= 5 hours

Practice ExercisePractice Exercise

4. The distance from manila to baguio is around 250 kilometers. a. Construct a function s, where s is the speed of travel that describes the time it takes to drive from manila to baguio? Since time is the qoutient of distance and speed we can write out the functions as t(s)