[PDF] [PDF] Chapter 9: Modeling Our World Lecture notes Math 1030 Section A

[PDF] Math 150 Lecture Notes Introduction to Functions - TAMU Math

The term function is used to describe a dependence of one quantity on another A function f is a rule that assigns to each element x in set A exactly one element, called f(x), in a set B The set A is called the domain of the function

[PDF] Module 1 Lecture Notes

17 Determining the Domain and Range of a Function Graphically 12 18 Reading the Math 111 Module 1 Lecture Notes Definition 1 A relation is a 

[PDF] LECTURE NOTES ON RELATIONS AND FUNCTIONS Contents 1

LECTURE NOTES ON RELATIONS AND FUNCTIONS PETE L CLARK Contents 1 Relations 1 11 The idea of a relation 1 12 The formal definition of a 

[PDF] MATH 221 FIRST SEMESTER CALCULUS

This is a self contained set of lecture notes for Math 221 The subject of this course is “functions of one real variable” so we begin by wondering what a real 

[PDF] Chapter 10 Functions

one to one and onto (or injective and surjective), how to compose functions, and when they are invertible Let us start with a formal definition Definition 63

[PDF] Part I: Sets, Functions, and Limits

they appeared at the end of the lecture, have been made and repro duced as " Lecture Notes" Consequently, as you proceed through an assignment, there is 

[PDF] Lecture Notes 2

Linear Functions (LECTURE NOTES 1) 1 Points, graphs and tables reading ability versus level of illumination Consider the following graph of the set of points  

[PDF] Chapter 9: Modeling Our World Lecture notes Math 1030 Section A

These relation ships are described by mathematical tools called functions Section A2 Language and Notation of Functions Definition of function A function 

[PDF] Lecture Notes in Calculus - Einstein Institute of Mathematics

Jul 10, 2013 · Lecture Notes in Calculus Raz Kupferman In this course we will cover the calculus of real univariate functions, which was developed during 

[PDF] Topic 1: Elementary Linear Functions Lecture Notes: section 11

If a student gets y= 80 for their final grade, how many hours per week did they study? Express x as a function of y The Inverse Function is x = (y 5) 15 solving 

[PDF] functions of flour in baking

[PDF] functions of ingredients worksheet

[PDF] functions of management pdf notes

[PDF] functions of mobile computing

[PDF] functions of propaganda

[PDF] functions of proteins

[PDF] functions of the nervous system

[PDF] functions of the respiratory system

[PDF] functions of the skin

[PDF] functions of theatre in society

[PDF] functions pdf

[PDF] functions pdf notes

[PDF] functions problems and solutions pdf

[PDF] fundamental analytical chemistry calculations

[PDF] fundamental of business intelligence grossmann w rinderle ma pdf

Chapter 9: Modeling Our World Lecture notes Math 1030 Section A Section A.1: Functions: the Building Blocks of MathematicalModels

Mathematical models

The purpose of amathematical modelis to represent something real (like economic changes) and help us to

understand it.

Mathematical models are based on the relationships betweenquantities that can change. These relation-

ships are described by mathematical tools calledfunctions.

Section A.2: Language and Notation of Functions

Definition of function

A function describes how a dependent variable changes with respect to one or more independent variables.

When there are only two variables, we often summarize them as an ordered pair with the independent variable first: (independent variable, dependent variable) We say that the dependent variable is a function of the independent variable. Ifxis the independent variable andyis the dependent variable, we write the function as y=f(x) 1 Chapter 9: Modeling Our World Lecture notes Math 1030 Section A Ex.1

Suppose we want to model the variation in temperature over the course of the day based on the data of

the following table:

TimeTemperatureTimeTemperature

6:00 a.m.50◦F1:00 p.m.73◦F

7:00 a.m.52◦F2:00 p.m.73◦F

8:00 a.m.55◦F3:00 p.m.70◦F

9:00 a.m.58◦F4:00 p.m.68◦F

10:00 a.m.61◦F5:00 p.m.65◦F

11:00 a.m.65◦F6:00 p.m.61◦F

12:00 a.m.70◦F

What is the dependent variable? What is the independent variable? Ex.2

For each situation, express the given function in words. Write the two variables as an ordered pair and

write the function with the notationy=f(x). (1) You are riding in a hot-air balloon. As the balloon rises,the surrounding atmospheric pressure decreases.

(2) You are on a barge headed south down the Mississippi River. You notice that the width of the river

changes as you travel southward with the current. 2 Chapter 9: Modeling Our World Lecture notes Math 1030 Section A

Section A.3: Representing Functions

How to represent a function

There are3basic ways to represent a function:

(1) We can represent a function with adata table. (2) We can draw a picture, orgraph, of a function. (3) We can write a compact mathematical representation of a function in the form of anequation.

The Coordinate Plane

Coordinates in the plane

The points in the coordinate plane are described by two coordinates: thex-coordinate gives the point"s

horizontal position relative to the origin, they-coordinate gives the point"s vertical position relative to the

origin.

We use thex-axis for the independent variable and they-axis for the dependent variable. The axes divide

the coordinate plane in4quadrants. 3 Chapter 9: Modeling Our World Lecture notes Math 1030 Section A

Section A.4: Creating Graphs of Functions

Definition of domain and range

Thedomainof a function is the set of values that both make sense and are of interest for the independent

variable. Therangeof a function consists of the value of the dependent variablethat correspond to the

values in the domain.

How to create graph of functions

Step 1: Identify the independent and dependent variables of the function.

Step 2: Identify the domain and the range of the function. Use this information to choose the scale and

labels on the axes. Zoom in on the region of interest to make the graph easier to read. Step 3: Make a graph using the given data. If appropriate, fill in the gaps between data points.

Step 4: before accepting any predictions of the model, be sure to evaluate the data and assumptions from

which the model was built. Ex.3

Do all the steps for Example 1.

4 Chapter 9: Modeling Our World Lecture notes Math 1030 Section A Ex.4

Imagine measuring the atmospheric pressure as you rise upward in the hot-air balloon. The table shows

typical values you might find for the pressure at the different altitudes, with the pressure given in units

of inches of mercury. This pressure unit is used with barometers, which measure pressure by the height

of a column of mercury.

AltitudePressure

030

5,00025

10,00022

20,00016

30,00010

Use these data to graph a function showing how atmospheric pressure depends on altitude. Use the

graph to predict atmospheric pressure at an altitude of15,000feet, and discuss the validity of your pre-

diction. 5quotesdbs_dbs14.pdfusesText_20