<< Chapter < Page Chapter >> Page >

Describing sets on the real-number line

Describe the intervals of values shown in [link] using inequality notation, set-builder notation, and interval notation.

Line graph of 1<=x<=3 and 5<x.

To describe the values, x , included in the intervals shown, we would say, “ x is a real number greater than or equal to 1 and less than or equal to 3, or a real number greater than 5.”

Inequality 1 x 3 or x > 5
Set-builder notation { x | 1 x 3 or x > 5 }
Interval notation [ 1 , 3 ] ( 5 , )

Remember that, when writing or reading interval notation, using a square bracket means the boundary is included in the set. Using a parenthesis means the boundary is not included in the set.

Got questions? Get instant answers now!
Got questions? Get instant answers now!

Given [link] , specify the graphed set in

  1. words
  2. set-builder notation
  3. interval notation
Line graph of -2<=x, -1<=x<3.

  1. values that are less than or equal to –2, or values that are greater than or equal to –1 and less than 3;
  2. { x | x 2 or 1 x < 3 } ;
  3. ( , 2 ] [ 1 , 3 )

Got questions? Get instant answers now!

Finding domain and range from graphs

Another way to identify the domain and range of functions is by using graphs. Because the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x -axis. The range is the set of possible output values, which are shown on the y -axis. Keep in mind that if the graph continues beyond the portion of the graph we can see, the domain and range may be greater than the visible values. See [link] .

Graph of a polynomial that shows the x-axis is the domain and the y-axis is the range

We can observe that the graph extends horizontally from −5 to the right without bound, so the domain is [ −5 , ) . The vertical extent of the graph is all range values 5 and below, so the range is ( −∞ , 5 ] . Note that the domain and range are always written from smaller to larger values, or from left to right for domain, and from the bottom of the graph to the top of the graph for range.

Finding domain and range from a graph

Find the domain and range of the function f whose graph is shown in [link] .

Graph of a function from (-3, 1].

We can observe that the horizontal extent of the graph is –3 to 1, so the domain of f is ( 3 , 1 ] .

The vertical extent of the graph is 0 to –4, so the range is [ 4 , 0 ) . See [link] .

Graph of the previous function shows the domain and range.
Got questions? Get instant answers now!
Got questions? Get instant answers now!

Finding domain and range from a graph of oil production

Find the domain and range of the function f whose graph is shown in [link] .

Graph of the Alaska Crude Oil Production where the y-axis is thousand barrels per day and the -axis is the years.
(credit: modification of work by the U.S. Energy Information Administration) http://www.eia.gov/dnav/pet/hist/LeafHandler.ashx?n=PET&s=MCRFPAK2&f=A.

The input quantity along the horizontal axis is “years,” which we represent with the variable t for time. The output quantity is “thousands of barrels of oil per day,” which we represent with the variable b for barrels. The graph may continue to the left and right beyond what is viewed, but based on the portion of the graph that is visible, we can determine the domain as 1973 t 2008 and the range as approximately 180 b 2010.

In interval notation, the domain is [1973, 2008], and the range is about [180, 2010]. For the domain and the range, we approximate the smallest and largest values since they do not fall exactly on the grid lines.

Got questions? Get instant answers now!
Got questions? Get instant answers now!

Given [link] , identify the domain and range using interval notation.

Graph of World Population Increase where the y-axis represents millions of people and the x-axis represents the year.

domain =[1950,2002] range = [47,000,000,89,000,000]

Got questions? Get instant answers now!

Questions & Answers

what is mutation
Janga Reply
what is a cell
Sifune Reply
how is urine form
Sifune
what is antagonism?
mahase Reply
classification of plants, gymnosperm features.
Linsy Reply
what is the features of gymnosperm
Linsy
how many types of solid did we have
Samuel Reply
what is an ionic bond
Samuel
What is Atoms
Daprince Reply
what is fallopian tube
Merolyn
what is bladder
Merolyn
what's bulbourethral gland
Eduek Reply
urine is formed in the nephron of the renal medulla in the kidney. It starts from filtration, then selective reabsorption and finally secretion
onuoha Reply
State the evolution relation and relevance between endoplasmic reticulum and cytoskeleton as it relates to cell.
Jeremiah
what is heart
Konadu Reply
how is urine formed in human
Konadu
how is urine formed in human
Rahma
what is the diference between a cavity and a canal
Pelagie Reply
what is the causative agent of malaria
Diamond
malaria is caused by an insect called mosquito.
Naomi
Malaria is cause by female anopheles mosquito
Isaac
Malaria is caused by plasmodium Female anopheles mosquitoe is d carrier
Olalekan
a canal is more needed in a root but a cavity is a bad effect
Commander
what are pathogens
Don Reply
In biology, a pathogen (Greek: πάθος pathos "suffering", "passion" and -γενής -genēs "producer of") in the oldest and broadest sense, is anything that can produce disease. A pathogen may also be referred to as an infectious agent, or simply a germ. The term pathogen came into use in the 1880s.[1][2
Zainab
A virus
Commander
Definition of respiration
Muhsin Reply
respiration is the process in which we breath in oxygen and breath out carbon dioxide
Achor
how are lungs work
Commander
where does digestion begins
Achiri Reply
in the mouth
EZEKIEL
what are the functions of follicle stimulating harmones?
Rashima Reply
stimulates the follicle to release the mature ovum into the oviduct
Davonte
what are the functions of Endocrine and pituitary gland
Chinaza
endocrine secrete hormone and regulate body process
Achor
while pituitary gland is an example of endocrine system and it's found in the Brain
Achor
what's biology?
Egbodo Reply
Biology is the study of living organisms, divided into many specialized field that cover their morphology, physiology,anatomy, behaviour,origin and distribution.
Lisah
biology is the study of life.
Alfreda
Biology is the study of how living organisms live and survive in a specific environment
Sifune
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply
Practice Key Terms 3

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Precalculus. OpenStax CNX. Jan 19, 2016 Download for free at https://legacy.cnx.org/content/col11667/1.6
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

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

Ask