A piecewise function is one that has different operations, depending on the values of the input
The piecewise function is;
[tex]g(x) = \begin{cases} -\left | x + 2 \right |&\mathbf{ \text{ if } -5 \leq x < 0 }\\ 2 \cdot x - 2 &\mathbf{ \text{ if } 0 < x \leq 2}\\ 2 &\mathbf{ \text{ if } 2 \leq x \leq 5}\end{cases}[/tex]
Reason:
The general form of the absolute value function is presented as follows;
[tex]f(x) = \mathbf{a \left | x - h \right | + k}[/tex]
The function given in the graph are;
Domain; -5 ≤ x < 0
Function; [tex]g(x) = -\left | x + 2 \right |[/tex]
Domain; 0 < x ≤ 2
Points on the graph are;
(0, -2), and (2, 2)
Slope = (2 - (-2))/(2 - 0) = 2
g(x) - (-2) = 2·(x - 0)
∴ Function; g(x) = 2·x - 2
Domain; 2 ≤ x ≤ 5
Function; g(x) = 2
Therefore, we have the following piecewise function;
[tex]g(x) = \mathbf{ \begin{cases} -\left | x + 2 \right |& \text{ if } -5 \leq x < 0 \\ 2 \cdot x - 2 & \text{ if } 0 < x \leq 2\\ 2 & \text{ if } 2 \leq x \leq 5\end{cases}}[/tex]
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See attached for the graphs of the various transformations of g(x).
• g(x) + 1 is a vertical shift upward by one unit
• g(x - 1) is a horizontal shift to the right by one unit
• -g(x) is a reflection across the x-axis
• 2g(x) is a scaling by a factor of 2
• -g(x - 1) is the composition of g(x - 1) and -g(x), hence a reflection and a horizontal shift
• |g(x)| leaves the positive parts of g(x) alone, and negates the negative parts (in other words, the parts of the graph of g(x) below the x-axis are reflected, the rest stays the same)
Mrs. Rodriquez has 24 students in her class. Ten of the students are boys. Jeff claims that the ratio of boys to girls in this class must be 5:12. What is Jeff’s error and how can he correct it? Jeff found the ratio of the number of boys to the total number of students. He needed to first find that there are 14 girls to get a ratio of 10:14 or 5:7.Jeff found the ratio of the number of boys to the total number of students. He needed to first find that there are 14 girls. The ratio would be 14:10 or 7:5.Jeff did not write the ratio in the correct order. He should have written it as 24:10.Jeff did not write the ratio in the correct order. He should have written it as 12:5.
Answer:
the answer is: A. Jeff found the ratio of the number of boys to the total number of students. He needed to first find that there are 14 girls to get a ratio of 10:14 or 5:7.
Explanation:
i got it right on a quiz i took and i looked up the question.
Answer:
a
Explanation:
Which of the following is one of the first things you
should do when preparing to
present yourself to employers?
-set your salary range
-gather references
-check your social media profile
-take a power point course
Answer:
I think gathering reference is a good idea.
What term refers to a person's thoughts matching his or her behavior?
attitude consistency
cognitive consistency
Individual consistency
social consistency
Answer:
cognitive consistency
Explanation:
.........
Answer:
cognitive consistency.
Explanation:
The table shows the types of information collected by a store regarding customer purchases. Which of the following data could be used in a geographical information system (GIS) to increase sales?
A geographical information system (GIS) is an information system that is used to manage data. They are also used to create and organize data. The total transaction amount can be used by the GIS to increase sales
From the attached table, we have the following data:
Zip code areaNumber of customersNumber of transactionsTotal transaction amountAmount per transactionThe usage of each data is as follows:
The zip code can be used to determine the region of the customers.
The number of customers and the number of transactions can be used to determine the rate of transactions per customer
We observe that, the total transaction amount is the product of the number of transactions and the amount per transaction.
This means that the total transaction amount is a summary of two other columns which deals directly with sales.
Information about total transaction amount can then be used independently to determine, predict and increase the sales of the store.
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¿crees que en pleno siglo xx1 los derechos de los niños, niñas y adolescentes se siguen vulnerando?¿porque?
Answer:
??????
Explanation:
i can't know this language
separated people based on the color of their skin.
2. I thought science would be uninteresting today, but the idea of
studying plant and animal cells
my attention.
3. "Please be a good
for your younger brother,"
reminded my mom. "He learns by watching your behavior."
4. It is a true Type here
that people would be treated bett
worce denending on the color of their skin
how did the environment shape seljuk empire?
Answer:
By the second quarter of the 13th century, the Seljuks had become an export nation, although they still imported more that they exported. They also developed many local industries and traded their own goods among the cities of the Empire. These industries included the production of alum and refined sugar.
Answer:
The Great Seljuk Empire emerged in the midst of division and chaos in the Islamic world. From migratory people, they transformed into conquerors that gave unity in the Middle East for a time. Some settled in a land they called their home even to this very day – Turkey
f(x)=2x^2-5x+1
help pleaseeeee!!
How did Christianity gain followers
Answer:
During the Roman Empire, Jesus of Nazareth began preaching a message of love and forgiveness. His life and teachings led to the rise of Christianity. The Romans at first persecuted Christians. In time, however, Christianity became the Roman Empire's official religion.
QUICK PAPER TO EDIT!! ASAP
I have a personal narrative due and was wondering if it flows, if i should change anything or if there is anything wrong with the grammar.
Answer:
uhmm u want someone to check it like 2nd person view check it.
Explanation:
x + 2x + 3x + 4x + 5x = 10 . Find x
Answer:
2/3
Explanation:
x + 2x + 3x + 4x + 5x = 10
=> 15x = 10
=> x = 10/15
=> x = 2/3
Which region is LEAST LIKELY to have a high physiological density?
Western Europe
East Asia
South Asia
Great Plains
China
Answer:
Great plains
Explanation:
1. Identify types of maps, the types of information presented in maps, and different kinds spatial patterns and
relationships maps can show. (1.1)
Words associated with biological (psychology)
Explanation:
Synonyms for biological psychologybi·o·log·i·cal psy·chol·o·gy
biological psychologynoun. Synonyms: biopsychology, psychobiology.
biological psychologynoun. The application of the principles of biology to the study of mental processes and behavior. Synonyms: biopsychology, psychobiology.pls mark me branilest
1. Which economy is NOT associated
with major, industrial world
economies?
Command
Market
Mixed
Traditional
Answer:
Traditional
Explanation:
cause it only deal with traditional things
paraphrase what Madison means by a republic in federalist no 10
The earliest civilizations developed between 4000 and 3000 BCE, when the rise of agriculture and trade allowed people to have surplus food and economic stability. Many people no longer had to practice farming, allowing a diverse array of professions and interests to flourish in a relatively confined area.
x/4 -6 = 2
can u solve this for me
Answer:
all divide with 4 to erase the denominator
x-24= 8
x=32
The length of a new rectangular playing field is 7 yards longer than triple the width. If the perimeter of the rectangular playing field is 438 yards, what are its dimensions?
Explanation:
L = 7+ 3W
the perimeter = 438
2(L+W) = 438
by using substitution :
2(7+3W+W) = 438
2(4W+7) = 438
4W+7 = 438/2
4W+7 = 219
4W = 219-7
4W = 212
W = 212/4 = 53
L = 7 + 3(53)
L = 7 + 159 = 166
so, the dimensions : the length = 166 yards
and the width = 53 yards
L = 7+ 3W
the perimeter = 438
2(L+W) = 438
by using substitution :
2(7+3W+W) = 438
2(4W+7) = 438
4W+7 = 438/2
4W+7 = 219
4W = 219-7
4W = 212
W = 212/4 = 53
L = 7 + 3(53)
L = 7 + 159 = 166
so, the dimensions : the length = 166 yards
and the width = 53 yards
What is the area of rectangular field?Width = w
triple the width = 3*w = 3w
Length = 7 yards longer than triple the width = 3w + 7
Perimeter = 438 yards
2*(length +width) = 438
2*(3w+ 7 + w) = 438 {Combine like terms}
2 * (4w + 7) = 438
2*4w +2*7 = 438 {Use distributive property}
8w + 14 = 438 {Subtract 14 from both side}
8w = 438 - 14
8w = 424 {Divide both sides by 8}
w = 424/8
w = 53 yards
Length = 3*53 +7 = 159 + 7 = 166 yards
Width = 53 yards
Length = 166 yards
The length and width of another rectangular field with same perimeter but a larger area is 80 m by 70 m.The perimeter of the existing field is
2(l + b)
= 2(90 + 60) = 2(150) = 300 yards
So we want another field having the same perimeter but a larger area.
Therefore, L = 7+ 3W
the perimeter = 438
2(L+W) = 438
by using substitution :
2(7+3W+W) = 438
2(4W+7) = 438
4W+7 = 438/2
4W+7 = 219
4W = 219-7
4W = 212
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Most energy used in the U.S. is produced from coal. There are 315,000,000 people in the U.S. It is estimated that one person is responsible for using 2000 lbs of coal per year. For every 100 lbs of coal burned, 2.5 lbs of sulfur go into the atmosphere. How much sulfur is put into the air by coal burning each year for all the people in the U.S.?
can one person make a difference in this world
According to the presentation, opportunities for which of the following jobs are expected to increase in the next ten years?
A. Reporter
B. Broadcast technician
C. Fine artist
D. Printer
Answer:
all of the above
Explanation:
According to Buddha, what is the “disease” of life?
what are two things Mr.Fraser suggested that people learn from this case?
Answer:
Become more effective with how we go about things to get more correct evidence and become more cautious about how accurate eyewitness testimonies are.
Explanation:
hey are u guys doing today i am doing good
Answer:
f I am doing fine gracias
What was the Confucian expectation for those who were superior in society?
Answer:
That the emperors should keep low taxes and administer justice.
The set of all whole numbers except 50 in set-builder notation
The set builder notation of all whole numbers except 50 is [tex]A = \mathbf{\{ x \in W \ | \ x \neq 50\}}[/tex]
the reason the set builder notation for the set of whole numbers is correct is as follows;
Set-builder notation is a notation in mathematics used for the description of a set including the enumeration of the set elements or the definition of a predicate based on the properties of the set members which is a formula of logic that gives a value of true for the members of the set and gives an evaluation of false for non members of the set
Therefore;
The set of all whole numbers except 50, A, in set builder notation is presented as follows;
[tex]A = \mathbf{\{ x \in W \ | \ x \neq 50\}}[/tex]
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Label each of the following as either a physical process or a
chemical process: (a) rusting of a metal can, (b) boiling a cup
of water, (c) pulverizing an aspirin, (d) digesting a candy bar,
(e) exploding of nitroglyerin.
Answer:
Rusting metal can: Chemical
Boiling water: Physical
Crushing aspirin: Physical
Exploding nitroglycerin: Chemical
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do any of you know Aidan Gallagher?
would you be interested in buying a sweat shirt to support him?
Answer:
Yes I know him.
Explanation:
Aidan Gallagher was born on September 18, 2003 is an American actor. His first major role was portraying one of the quadruplets, Nicky Harper, in the Nickelodeon comedy television series Nicky, Ricky, Dicky & Dawn.
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College Algebra:
Determine whether the given equation is linear or nonlinear.
2x - 7 = πx - 5
Answer:
nonliner
Explanation:
2x - 7 = πx - 5= A nonlinear equation has the degree as 2 or more than 2, but not less than 2.
what did europenas gain from the indians that proved more important than gold
Answer:
Hi, there!
Europeans learned new agricultural techniques and discovered new crops, like maize (corn)
Explanation:
