Directions and Analysis
Task 1: Functions and Transformations
Transformations can be thought of as functions that take the points from one object (the pre-
image) to the corresponding points on another object (the image). In the unit, you saw
examples of how algebra can be used to rewrite the coordinates of points after they have
been transformed. You can also use function notation to rewrite the coordinates. For
example, these statements show several different ways you can use function notation for the
translation, T, of a point 6 units in the positive x-direction:
• T(x, y) = (x + 6, y)
T:(, y) = (x + 6, y)
• T<6, 0>(x, y) = (x + 6, y)
16. o(x, y) = (x + 6, 9)
.
a. Write functions for the following transformations using function notation. Choose a
different letter to represent each function. For example, you can use R to represent
rotations. Assume that a positive rotation occurs in the counterclockwise direction.
translation of a units to the right and b units up
reflection across the y-axis
reflection across the x-axis
rotation of 90 degrees counterclockwise about the origin, point o
rotation of 180 degrees counterclockwise about the origin, point o
rotation of 270 degrees counterclockwise about the origin, point o

Answers

Answer 1

Functions for the following transformations are to be written using function notation:

A translation of a units to the right and b units up is  T< a, b>(x, y) = (x + a, y + b).

Here, a units is translated to the right and b units are translated up.

- Reflection across the y-axis is R(x, y) = (-x, y).The y-coordinates remain constant, but the x-coordinates are reflected.

- Rotation of 90 degrees counterclockwise about the origin is R(x, y) = (-y, x).The point (x, y) becomes (-y, x) after the rotation of 90 degrees counterclockwise about the origin.

- Reflection across the x-axis is R(x, y) = (x, -y).The x-coordinates remain constant, but the y-coordinates are reflected.

- Rotation of 180 degrees counterclockwise about the origin is R(x, y) = (-x, -y).The point (x, y) becomes (-x, -y) after the rotation of 180 degrees counterclockwise about the origin.

- Rotation of 270 degrees counterclockwise about the origin is R(x, y) = (y, -x).The point (x, y) becomes (y, -x) after the rotation of 270 degrees counterclockwise about the origin.

For more such questions on function notation visit:

https://brainly.com/question/27915724

#SPJ8


Related Questions

Activities:
1. Give the name and year of TWO hurricanes that have passed through and affected the
Caribbean.
2. Briefly explain why hurricanes occur in the Caribbean.

Answers

Answer:

1. Hurricane Gilbert year was 1951. Hurricane Irma year was 2017

2. The Caribbean has warm water and moist air in the Summers which is what triggers hurricanes to happen. So that is why the Caribbean is so prone to hurricanes.

Explanation:

(Have a great day)

Please let me know !! ASAP PLS

Answers

Answer:

[tex]AD = 8[/tex], [tex]DC = 15[/tex], [tex]m\,\angle A = 112^{\circ}[/tex], [tex]m\,\angle B = 68^{\circ}[/tex], [tex]m\,\angle C = 112^{\circ}[/tex]

Explanation:

If the quadrilateral presented in figure is a parallelogram, then the following conditions are satisfied:

[tex]AD = BC[/tex] (1)

[tex]AB = DC[/tex] (2)

[tex]m\,\angle D = m\,\angle B[/tex] (3)

[tex]m\,\angle A = m\,\angle C[/tex] (4)

[tex]m\,\angle A + m\,\angle B = 180^{\circ}[/tex] (5)

[tex]m\,\angle C + m\,\angle D = 180^{\circ}[/tex] (6)

If we know that [tex]m\,\angle D = 68^{\circ}[/tex], [tex]AB = 15[/tex] and [tex]BC = 8[/tex], then we have the following results:

[tex]AD = 8[/tex], [tex]DC = 15[/tex], [tex]m\,\angle A = 112^{\circ}[/tex], [tex]m\,\angle B = 68^{\circ}[/tex], [tex]m\,\angle C = 112^{\circ}[/tex]

The central Location of India at the head
of the Indian Oceanis considered of great
significance.why?​

Answers

Answer: The trans-Indian Ocean routes which connect the countries of Europe in the West and the countries of East Asia provide a strategic central location to India.

Explanation: Hope this helped!

How far is it from March to June?​

Answers

3 months between march to june

From March to June, there are three months, so it is a span of approximately 90 days or a quarter of a year. The exact number of days can vary depending on the specific calendar year and any leap days within that period.

Leap days, occurring in the Gregorian calendar, are additional days added to February every four years to synchronize the calendar with Earth's orbit around the sun.

This adjustment accounts for the fact that a complete orbit takes about 365.2425 days. Leap years, such as 2020 and 2024, have 366 days instead of the usual 365.

Leap days help to maintain the alignment of seasons and prevent the gradual shifting of dates. They play a crucial role in ensuring that our calendar remains accurate and aligned with astronomical cycles, promoting long-term consistency and reliability in timekeeping.

Learn more about leap days here:

https://brainly.com/question/28996032

#SPJ6

SOMEONE HELP ASAP✋. 4. As Buddhism diffused through East Asia,
Buddhist traditions blended with local cultural
customs to create distinct religious practices,
such as Daoism in China and Shinto in Japan.
Which of the following terms best describes this
blending of cultural traditions?
(A) Assimilation
(B) Acculturation
(C) Possibilism
(D) Multiculturalism
(E) Syncretism

Answers

Answer:

Option E, Syncretism

Explanation:

Syncretism depicts blending of thoughts, culture and religion. For example

- in the Rastafarian movement in Jamaica, African-Hebrew and Christian religious blended with the Caribbean freed slave culture to make a unique culture.

The same is the case as depicted in the question where Buddhism got mixed with the  Daoism in China and Shinto in Japan

Hence, option E is correct

is global media a friend of foe? why?​

Answers

Answer:

Both

Explanation:

It's behaviour depends on our usage.

B. freezing
A. evaporating
C. melting D. mixing
5. When water turns into ice, Which phase change is involved?
B. condensation
A. evaporation
C. deposition D.freezing​

Answers

Answer:

D

Explanation:

water freezes and turns into ice

D Freezing because the particles are slowing down

tropic of cancer who did invent and which year? ​

Answers

tropic cancer was invented by Obelisk Pess in Paris, Fance in 1934

ghatta wheeling technology​

Answers

What does this mean I don’t understand
whatttt????
Are you trying to say

HELP ASAP!!!! What conclusion can you make about the connection between precipitation patterns and population density in China?

Answers

Answer:

c

Explanation:

There is a connection. The maps show the highest density of people in the areas with greatest rainfall. Southeast China has the highest rainfalls and the highest population density.

Exact answer from Plato (Edmentum). Hope this helps luvs <3

Winds are turned to the right in the Northern Hemisphere. true or false

Answers

In the Northern Hemisphere, winds curve to the right because of the Earth’s rotation. Saying that, the Southern Hemisphere will curve to the left. :)

Last minute Help me out please and thank you!

How are you and your local community connected to other people and religions and faith
traditions in the world?

Answers

Answer:

As much as religious conflict dominates our public ... We asked five students of religion how faith builds ... to other people by the Catholic Church – or, more accurately...

What causes the possible scenario to happen? Explain your answer.

Answers

Answer:

A Scenario is a set of values that Excel saves and can substitute automatically on your worksheet. You can create and save different groups of values as scenarios and then switch between these scenarios to view the different results.

Use Scenario Analysis to predict potential outcomes of your desired strategies or ... Then look at the timescale in which it will happen

POSS
Use the following diagram to answer the question below.
G
Earth's orbit
H
F
Equator
E
A
Sun
B
D
С
Which of the following positions is experiencing winter in the southern hemisphere?
Position E
Position c
Position A
Position G

Answers

The correct answer is B. Position C.

Explanation

The image shows the translation of the Earth in which the different stations are shown according to the position of the Earth concerning the sun. Position A represents the equinox of March 21 in which the northern hemisphere is in the spring season, while the southern hemisphere is in autumn. Position C represents the solstice on June 21 in which the northern hemisphere is in summer, while the southern hemisphere is in winter. Position E represents the equinox of September 23 in which the northern hemisphere is in autumn, while the southern hemisphere is in spring. In position G it represents the solstice of December 21 in which the northern hemisphere is in winter, while the southern hemisphere is in summer. Therefore, the correct answer is C.

I need the answer to this ASAP .thank you

Answers

Convection then mantle

Z is the mantle

What is commercial farming​

Answers

the production of crops and farm animals for sale, usually with the use of modern technology: commercial farming methods.

What would you have done if you had bet on the lottery and had won?​

Answers

Answer:

Consult With the Professionals You Hired. These professionals exist to help you, not the other way around. ...

Pay Off Most Debts. ...

Start an Emergency Fund. ...

Put Away Money for Retirement. ...

Diversify Your Investments. ...

Set Up College Funds. ...

Give to Those Less Fortunate. ...

Learn to Say No.

Explanation:

hope i helpeld

How do you involve different community members into planning and decision-making process?​

Answers

Answer:

5 ways to get employees involved in decision-making

Form a committee. Once a company reaches a certain size, it can be hard to hear everyone's voice. ... Suggestion box. Another way to help engage your workers is by encouraging them to suggest changes that should be made to the company. ... Offer choices. ... Let them choose their training. ... Remove set work hours.

Invite – Include – Inspire. Wise leaders know that collaborative practices like participatory planning and decision-making are not only respectful – they are the best route to creating communities, or organizations, that thrive. Collaborative leaders understand that leading from behind is not giving up control.Community participation can be loosely defined as the involvement of people in a commu- nity in projects to solve their own problems. ... Community participation is especially important in emergency sanitation programmes where people may be unaccustomed to their surroundings and new sanitation facilities.

Hopefully u will satisfy with my answer of ur question..!!Have a nice day ahead dear..!!

How do you involve people in decision making?
5 ways to get employees involved in decision-making
Form a committee. Once a company reaches a certain size, it can be hard to hear everyone's voice. ...
Suggestion box. Another way to help engage your workers is by encouraging them to suggest changes that should be made to the company. ...
Offer choices. ...
Let them choose their training. ...
Remove set work hours.

how does the sun rise water but it can also drain water

Answers

Answer:

the sun evaporates the water and the water rises. clouds collect the water and when it becomes heavy, the water falls as rain. I don't know how the sun can drain water.

Explanation:

What are 3 least things that people could do help them prepare for valcanoes earthquakes, or tsunami?

Answers

Answer:

Evacuate to another location before the event takes a turn for the worst!

Explanation:

purposes of launching artificial satellite​

Answers

Answer:

Artificial satellites are used to study the Earth, other planets, to help us communicate, and even to observe the distant Universe. Satellites can even have people in them, like the International Space Station and the Space Shuttle. The first artificial satellite was the Soviet Sputnik 1 mission, launched in 1957.

The study the earth and is climate as well as to spy on other countries and study the universe

Which of these is an impact of noise pollution?
O A. high life expectancy
B.
more trees
OC.
hypertension
D.
low levels of poverty

Answers

Answer:

c i think

..................................................

Answer:

A is right I think...........................

What is most likely true of all the strata from the Jurassic Period?

Answers

Answer:

Mostly because I 8N to fit into what am currently doing in actuality years

Answer:

It’s B- they contain similar fossils

Explanation:

Why is is nunavut a separate territory?

Answers

Nunavut was situated in the Northwest Territories and was later separated due to Nunavut Land Claims Agreement that was fed out of the self-government movement started in 1971[14].


1. What is an air mass?
2. Briefly explain how the northern hemispheric winter affects the Caribbean.​

Answers

Answer:

I don't know the answer but I was wondering if you can help me with mine

the median of 2,2,5,1,6,77​

Answers

Answer:1 will be the answer

Explanation:

Answer:

56

Explanation:

this is not a right answer but i try taat

10 point The diagram below shows four phases of the moon as it revolves around Earth. A student builds a model based on this diagram. The student uses foam balls to represent the moon and Earth and a flashlight to represent the sun. The student should shine the flashlight on the model of Earth from Position-​

Answers

Answer:

4

Explanation:

Answer: the answer is 4

Explanation:

What is Landscape evolution theory

Answers

Answer:

Landscape evolution theories indicate that the topography inherently records the interaction between climatic, tectonic, and surface processes. ... Rather than focusing on empirical relationships, landscape-evolution modeling attempts to formalize the understanding of process mechanics and systems coupling.

The atmospheric system of pressure and winds is intimately related to the oceanic system. The frictional drag of winds is among the driving forces of ocean currents.

a. True
b. False

Answers

Answer:

Area Practice Worksheet

Find the area of the following triangles using the formula: B stands for base, the bottom of the triangle. H stands for height, which is the height or how tall the triangle is.

Explanation:Area Practice Worksheet

Find the area of the following triangles using the formula: B stands for base, the bottom of the triangle. H stands for height, which is the height or how tall the triangle is.

Which of the following is not an example of predation?
a.
A blue whale feeding on zooplankton
b.
A tree obtaining nutrients from the soil
c.
A caterpillar eating the leaves of a tree
d.
A wolf eating a deer

Answers

B. A tree obtaining nutrients from the soil

Answer:

b

Explanation:

Other Questions
What were hitler's views about German Race Dennis buys 32 inches of trim for a craft project. What fraction of a yard does Dennis buy? PLEASE HURRYThe narration portrays the Wolf family as caring. How might the characterization of the wolves be different if Shere Khan were the narrator? The wolves would be seen as hardworking, because Shere Khan admires them.The wolves would be seen as friendly, because they are Shere Khans neighbors.The wolves would be seen as a threat, because the animals are enemies. Aaron bought a stereo system for $55 and spends $8.45 on parts. He sells the system for$60. What is his profit/loss? What type of organism is the common house cat?FparasiteGsaprophyteHautotrophJheterotroph what is 3c-9d+7c+5d simplified Sexton, Corp., has projected the following sales for the coming year: Q1 Q2 Q3 Q4 Sales $ 860 $ 940 $ 900 $ 1,000 Sales in the year following this one are projected to be 15 percent greater in each quarter. a. Calculate payments to suppliers assuming that the company places orders during each quarter equal to 30 percent of projected sales for the next quarter. Assume that the company pays immediately. (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.) b. Calculate payments to suppliers assuming a 90-day payables period. (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.) c. Calculate payments to suppliers assuming a 60-day payables period. Pls Help Asap pls T^T What is the difference between present and future? write two examples of consumers tell whether they are herbivores omnivores carnivors or scavengers Plzzzz guys help me with this i dont know 3. Bacteria can multiply at an alarming rate when eachbacteria splits into two new cells, doubling. If we startwith only 3 bacteria which can double every hour, howmany bacteria will we have by half the day? why did the oil fields close during the great depression? 1. Determine the pH of the following solutions:a. 1 x 10-3 M HCI Weight of three books are 234 kg, 356 kg and 238 kg. Find the total weight of all the three books. How do the authors of Ads: Why We Buy What We Buy, convey their purpose of helping readers understand the effectiveness of advertising? They describe the large sizes of supermarket shopping carts. They show how one quarter seemed to be worth more than an identical quarter. They discuss the wide variety of products available in stores. They explain that students remember slogans better than poems they've studied. You have 2.2 mol Xe and 2.1 mol F2, but when you carry out thereaction you end up with only 0.25 mol XeFg. What is the percentyield of this experiment?Xe(g) + 2 F2 (g) XeF, (g) Can someone please tell me the answers How does computer applications affect our lives daily? 1- paragraph (4 sentences) HELP I WILL GIVE BRAINLIEST! FLVS! PLEASE HELP ME! Read and match the sentence with its correct pronoun.Match Term DefinitionTus padres y t viven en una casa en Tegucigalpa. A) YoUn grupo de estudiantes de Costa Rica mira la tele en su casa en Miami. B) UstedesSoy Lidia. Ayudo a su madre y a su to en la cocina. C) lLos equipos de Juan y Rufino practican los martes y los jueves. D) Ellos