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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
Discuss the differences between taste and flavor, including how other sensory inputs contribute to our perception of flavor.
taste refers to your understanding of the flavor . while flavor one The other hand is refers to sort of just a blend things.
Faith
While taste primarily relies on our taste buds, flavor involves a complex interplay between taste and aroma
Kamara
which drugs can we use for ulcers
Omeprazole
Cimetidine / Tagament
For the complicated once ulcer - kit
Patrick
what is the function of lymphatic system
to drain extracellular fluid all over the body.
asegid
The lymphatic system plays several crucial roles in the human body, functioning as a key component of the immune system and contributing to the maintenance of fluid balance. Its main functions include:
1. Immune Response: The lymphatic system produces and transports lymphocytes, which are a type of
asegid
to transport fluids fats proteins and lymphocytes to the blood stream as lymph
Adama
Anatomy is the identification and description of the structures of living things
Kamara
what's the difference between anatomy and physiology
Anatomy is the study of the structure of the body, while physiology is the study of the function of the body. Anatomy looks at the body's organs and systems, while physiology looks at how those organs and systems work together to keep the body functioning.
AI-Robot
what is enzymes all about?
Enzymes are proteins that help speed up chemical reactions in our bodies. Enzymes are essential for digestion, liver function and much more. Too much or too little of a certain enzyme can cause health problems
Kamara
how does the stomach protect itself from the damaging effects of HCl
little girl okay how does the stomach protect itself from the damaging effect of HCL
Wulku
it is because of the enzyme that the stomach produce that help the stomach from the damaging effect of HCL
Kamara
function of digestive system
function of digestive
Ali
what is the normal body temperature
please why 37 degree selcius normal temperature
Mark
the normal temperature is 37°c or 98.6 °Fahrenheit is important for maintaining the homeostasis in the body
the body regular this temperature through the process called thermoregulation which involves brain skin muscle and other organ working together to maintain stable internal temperature
Stephanie
anaemia is the decrease in RBC count hemoglobin count and PVC count
Eniola
what is the pH of the vagina
how does Lysin attack pathogens
Diya
I information on anatomy position and digestive system and there enzyme
anatomy of the female external genitalia
Organ Systems Of The Human Body (Continued)
Organ Systems Of The Human Body (Continued)
what's lochia albra
Kizito
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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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