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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.
- Consider the equation
. If we are free to choose values for
, then
would be considered the independent variable. Since the value of
depends on the value of
,
would be the dependent variable.
- Consider the equation
. If we are free to choose values for both
and
, then
and
would be considered independent variables. Since the value of
depends on the values chosen for
and
,
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.
, where
is the independent variable.
Any number except 0 can be substituted for
and yield a meaningful result. Hence, the domain is the collection of all real numbers except 0.
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, where
is the independent variable and the equation relates time,
, and distance,
.
It makes little sense to replace
by a negative number, so the domain is the collection of all real numbers greater than or equal to 0.
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, where the independent variable is
.
The letter
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.
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, where the independent variable is
.
We can replace
by any real number and the expression
is computable. Hence, the domain is the collection of all real numbers.
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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.
, where this equation relates the distance an object falls,
, to the time,
, it has had to fall.
all real numbers greater than or equal to 0
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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.
Exercises for review
Questions & Answers
it is the relatively stable flow of income
what is circular flow of income
branches of macroeconomics
what is Flexible exchang rate?
is gdp a reliable measurement of wealth
introduction to econometrics
Why is unemployment rate never zero at full employment?
bcoz of existence of frictional unemployment in our economy.
Umashankar
what is flexible exchang rate?
poudel
due to existence of the pple with disabilities
Abdulraufu
the demand of a good rises, causing the demand for another good to fall
is it possible to leave every good at the same level
Joseph
I don't think so. because check it, if the demand for chicken increases, people will no longer consume fish like they used to causing a fall in the demand for fish
Anuolu
is not really possible to let the value of a goods to be same at the same time.....
Salome
Suppose the inflation rate is 6%, does it mean that all the goods you purchase will cost
6% more than previous year? Provide with reasoning.
Not necessarily. To measure the inflation rate economists normally use an averaged price index of a basket of certain goods. So if you purchase goods included in the basket, you will notice that you pay 6% more, otherwise not necessarily.
Waeth
discus major problems of macroeconomics
what is the problem of macroeconomics
Yoal
Economic growth
Stable prices
and low unemployment
Ephraim
explain inflationcause and itis degre
increase in general price levels
WEETO
Good day
How do I calculate this question: C= 100+5yd G= 2000 T= 2000 I(planned)=200.
Suppose the actual output is 3000. What is the level of planned expenditures at this level of output?
how to calculate actual output?
Chisomo
how to calculate the equilibrium income
Beshir
Criteria for determining money supply
who we can define macroeconomics in one line
Muhammad
Aggregate demand
Mohammed
C=k100 +9y and i=k50.calculate the equilibrium level of output
nawalparasi district
from belatari
Amisha
I am Camara from Guinea west Africa... happy to meet you guys here
Sekou
ahile becheclor ho
Amisha
hjr ktm bta ho
ani k kaam grnu hunxa tw
Amisha
money as unit of account means what?
Kalombe
A unit of account is something that can be used to value goods and services and make calculations
Jim
all of you please speak in English I can't understand you're language
Muhammad
I want to know how can we define macroeconomics in one line
Muhammad
it must be .9 or 0.9
no Mpc is greater than 1
Y=100+.9Y+50
Y-.9Y=150
0.1Y/0.1=150/0.1
Y=1500
Kalombe
Mercy is it clear?😋
Kalombe
hi can someone help me on this question
If a negative shocks shifts the IS curve to the left, what type of policy do you suggest so as to stabilize the level of output?
discuss your answer using appropriate graph.
if interest rate is increased this will will reduce the level of income shifting the curve to the left ◀️
Kalombe
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Source:
OpenStax, Elementary algebra. OpenStax CNX. May 08, 2009 Download for free at http://cnx.org/content/col10614/1.3
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