<< Chapter < Page Chapter >> Page >
This module is from Elementary Algebra by Denny Burzynski and Wade Ellis, Jr. Operations with algebraic expressions and numerical evaluations are introduced in this chapter. Coefficients are described rather than merely defined. Special binomial products have both literal and symbolic explanations and since they occur so frequently in mathematics, we have been careful to help the student remember them. In each example problem, the student is "talked" through the symbolic form.Objectives of this module: be able to identify the independent and dependent variables of an equation, be able to specify the domain of an equation.

Overview

  • Independent and Dependent Variables
  • The Domain of an Equation

Independent and dependent variables

Independent and dependent variables

In an equation, any variable whose value can be freely assigned is said to be an independent variable. Any variable whose value is determined once the other values have been assigned is said to be a dependent variable. Two examples will help illustrate these concepts.

  1. Consider the equation y = 2 x 7 . If we are free to choose values for x , then x would be considered the independent variable. Since the value of y depends on the value of x , y would be the dependent variable.
  2. Consider the equation m = 4 g k 2 . If we are free to choose values for both g and k , then g and k would be considered independent variables. Since the value of m depends on the values chosen for g and k , m would be the dependent variable.

The domain of an equation

Domain

The process of replacing letters with numbers is called numerical evaluation. The collection of numbers that can replace the independent variable in an equation and yield a meaningful result is called the domain of the equation. The domain of an equation may be the entire collection of real numbers or may be restricted to some subcollection of the real numbers. The restrictions may be due to particular applications of the equation or to problems of computability.

Sample set a

Find the domain of each of the following equations.

y = 2 x , where x is the independent variable.

Any number except 0 can be substituted for x and yield a meaningful result. Hence, the domain is the collection of all real numbers except 0.

Got questions? Get instant answers now!

d = 55 t , where t is the independent variable and the equation relates time, t , and distance, d .

It makes little sense to replace t by a negative number, so the domain is the collection of all real numbers greater than or equal to 0.

Got questions? Get instant answers now!

k = 2 w w 4 , where the independent variable is w .

The letter w can be replaced by any real number except 4 since that will produce a division by 0. Hence, the domain is the collection of all real numbers except 4.

Got questions? Get instant answers now!

a = 5 b 2 + 2 b 6 , where the independent variable is b .

We can replace b by any real number and the expression 5 b 2 + 2 b 6 is computable. Hence, the domain is the collection of all real numbers.

Got questions? Get instant answers now!

Practice set a

Find the domain of each of the following equations. Assume that the independent variable is the variable that appears in the expression on the right side of the " = " sign.

y = 5 x + 10

all real numbers

Got questions? Get instant answers now!

y = 5 x

all real numbers except 0

Got questions? Get instant answers now!

y = 3 + x x

all real numbers except 0

Got questions? Get instant answers now!

y = 9 x 6

all real numbers except 6

Got questions? Get instant answers now!

m = 1 n + 2

all real numbers except 2

Got questions? Get instant answers now!

s = 4 9 t 2 , where this equation relates the distance an object falls, s , to the time, t , it has had to fall.

all real numbers greater than or equal to 0

Got questions? Get instant answers now!

g = 4 h 7 21

all real numbers

Got questions? Get instant answers now!

Exercises

For the following problems, find the domain of the equations. Assume that the independent variable is the variable that appears in the expression to the right of the equal sign.

y = 4 x + 7

x = all real numbers

Got questions? Get instant answers now!

y = x 2 + 2 x 9

x = all real numbers

Got questions? Get instant answers now!

y = 11 x

x = all real numbers

Got questions? Get instant answers now!

y = 3 x

x = all real numbers except zero

Got questions? Get instant answers now!

m = 16 h

h = all real numbers except zero

Got questions? Get instant answers now!

t = 5 s 6

s = all real numbers except 6

Got questions? Get instant answers now!

Exercises for review

( [link] ) Name the property of real numbers that makes 4 y x 2 = 4 x 2 y a true statement.

commutative property of multiplication

Got questions? Get instant answers now!

( [link] ) Simplify x 5 n + 6 x 4 .

Got questions? Get instant answers now!

( [link] ) Supply the missing phrase. Absolute value speaks to the question of and not "which way."

"how far"

Got questions? Get instant answers now!

( [link] ) Find the product. ( x 8 ) 2 .

Got questions? Get instant answers now!

( [link] ) Find the product. ( 4 x + 3 ) ( 4 x 3 ) .

16 x 2 9

Got questions? Get instant answers now!

Questions & Answers

how does Neisseria cause meningitis
Nyibol Reply
what is microbiologist
Muhammad Reply
what is errata
Muhammad
is the branch of biology that deals with the study of microorganisms.
Ntefuni Reply
What is microbiology
Mercy Reply
studies of microbes
Louisiaste
when we takee the specimen which lumbar,spin,
Ziyad Reply
How bacteria create energy to survive?
Muhamad Reply
Bacteria doesn't produce energy they are dependent upon their substrate in case of lack of nutrients they are able to make spores which helps them to sustain in harsh environments
_Adnan
But not all bacteria make spores, l mean Eukaryotic cells have Mitochondria which acts as powerhouse for them, since bacteria don't have it, what is the substitution for it?
Muhamad
they make spores
Louisiaste
what is sporadic nd endemic, epidemic
Aminu Reply
the significance of food webs for disease transmission
Abreham
food webs brings about an infection as an individual depends on number of diseased foods or carriers dully.
Mark
explain assimilatory nitrate reduction
Esinniobiwa Reply
Assimilatory nitrate reduction is a process that occurs in some microorganisms, such as bacteria and archaea, in which nitrate (NO3-) is reduced to nitrite (NO2-), and then further reduced to ammonia (NH3).
Elkana
This process is called assimilatory nitrate reduction because the nitrogen that is produced is incorporated in the cells of microorganisms where it can be used in the synthesis of amino acids and other nitrogen products
Elkana
Examples of thermophilic organisms
Shu Reply
Give Examples of thermophilic organisms
Shu
advantages of normal Flora to the host
Micheal Reply
Prevent foreign microbes to the host
Abubakar
they provide healthier benefits to their hosts
ayesha
They are friends to host only when Host immune system is strong and become enemies when the host immune system is weakened . very bad relationship!
Mark
what is cell
faisal Reply
cell is the smallest unit of life
Fauziya
cell is the smallest unit of life
Akanni
ok
Innocent
cell is the structural and functional unit of life
Hasan
is the fundamental units of Life
Musa
what are emergency diseases
Micheal Reply
There are nothing like emergency disease but there are some common medical emergency which can occur simultaneously like Bleeding,heart attack,Breathing difficulties,severe pain heart stock.Hope you will get my point .Have a nice day ❣️
_Adnan
define infection ,prevention and control
Innocent
I think infection prevention and control is the avoidance of all things we do that gives out break of infections and promotion of health practices that promote life
Lubega
Heyy Lubega hussein where are u from?
_Adnan
en français
Adama
which site have a normal flora
ESTHER Reply
Many sites of the body have it Skin Nasal cavity Oral cavity Gastro intestinal tract
Safaa
skin
Asiina
skin,Oral,Nasal,GIt
Sadik
How can Commensal can Bacteria change into pathogen?
Sadik
How can Commensal Bacteria change into pathogen?
Sadik
all
Tesfaye
by fussion
Asiina
what are the advantages of normal Flora to the host
Micheal
what are the ways of control and prevention of nosocomial infection in the hospital
Micheal
what is inflammation
Shelly Reply
part of a tissue or an organ being wounded or bruised.
Wilfred
what term is used to name and classify microorganisms?
Micheal Reply
Binomial nomenclature
adeolu
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Elementary algebra. OpenStax CNX. May 08, 2009 Download for free at http://cnx.org/content/col10614/1.3
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Elementary algebra' conversation and receive update notifications?

Ask