PLZZZ HELP ITS DUE VERY SOON!
Write a function to represent each series of transformations:
• rotation of 90 degrees counterclockwise about the origin, point O, then a reflection across the x-axis
• reflection across the y-axis, then a translation a units to the right and b units up
• translation a units to the right and b units up, then a rotation of 180 degrees counterclockwise about the origin, then a reflection across the y-axis ​

Answer:

Step-by-step explanation:

For the first one, I believe you would need to use a rotation matrix; to rotate 90º counterclockwise, the matrices would look like ; you would then multiply those out. A reflection across the x-axis would be changing the sign of f(x) (from negative to positive or positive to negative), a reflection across the y-axis would be changing the sign of x, translation a units to the right would be subtracting a from x, translation b units up would be adding b to x. Rotation of 180º about the origin would be the same format as the first matrix, except it would be cos180 and cos0 on the top and sin180 sin0 on the bottom. Reflection across the y-axis would be changing the sign of x again.

OR

1. We know that, 'Translation shifts the figure in any direction'.

As, the function f(x) is translated 'a' units to the right, the new form of function is f(x-a).

Again, the function is translated 'b' units up, the final form of the function is f(x-a)+b.

2 and 3. We know that, ' Reflection flips the image over a line'.

As the function g(x) is reflected over y-axis, the new form of the function is g(-x).

As the function h(x) is reflected over x-axis, the new form of the function is -h(x).

4 , 5 and 6. We know that, 'Rotation turns the image around a point to a certain degree'.

Let us assume the function to be a point (x,y).

As the function is rotated by 90° counterclockwise about the origin, the new function becomes ( y,-x ) i.e. R_{90}R

90

(x,y) = ( -y,x ).

As the function is rotated by 180° counterclockwise about the origin, the new function becomes ( y,-x ) i.e. R_{180}R

180

(x,y) = ( -x,-y ).

As the function is rotated by 2700° counterclockwise about the origin, the new function becomes ( y,-x ) i.e. R_{270}R

270

(x,

What is the y-intercept of the graph of the line given by the equation 3y + 4x = 15
A. 5
B. 4
C. 3
D. -4/3

A pump moves 70 gallons of water
per minute. How long will it take the
pump to empty a 2,030-gallon tank?

What's the maximum amount of money you should spend on a Modern Art painting worth 30k if you had to pay 15% tax?

Please help!!
Will mark brainliest

Simplify the following expression.
3^3/5• 3^(-7/5)

Niall hikes 250.6 meters up a mountain. If he is 70% of the way up, how many meters tall is the mountain?

what is the volume of a rectangular prism with a length of 5 cm, a height of 3 cm, and a width of 10 cm?

It is in the picture Thanks :D

A flying squirrel's nest is 6 meters high in a tree. From its nest, the flying squirrel glides 8 meters to reach an acorn that is on the ground. How far is the acorn from the base of the tree? If necessary, round to the nearest tenth.

What is the solution of the system? {5x−y=−21x+y=−3 Enter your answer in the boxes. ( , )

please help√√√:-) 1111

what is the unit price of cheese if 1.6 pounds cost $14.40?

1.
Gina buys a new TV for $999.00. She buys during a promotion at the store where she gets a 12
percent discount. She will also pay eight percent in sales tax.
True or false: Gina will pay eight percent in tax on $999.00, the price of the TV.

options:

O True
O False

A pencil pouch has 12 pencils and 30 led pencils, What is the ratio of
pencils to led pencils?

Damell had 27 coins in his pocket. He lost some. Write an expression that shows how many coins Darell lost.
A.27 -
B. n - 27
C. 27+n
D.n+27

What is the price of $45 art set with 7% tax

PLEASE HELP! ITS DUE TODAY!!!

Alicia borrowed $3000 from the bank at a rate of 12% simple interest per year. How much TOTAL did she pay the bank back after 5 years? (Hint: do NOT add the amount back to the money she borrowed)

help for brainlest what can be use ti

Lupita y Fernando y Andrés quieren comprar entre los tres una bicicleta que ven todos los días en el aparador de la tienda todo para todos para sus vacaciones le han deseado tanto que decidieron comprarla cada uno sacó cuentas de lo que debería pagar por la bicicleta​

On a coordinate plane, the coordinates of vertices R and T for a polygon are R(−7, 3) and T(3, 3). What is the length of Side RT of the polygon?


4 units

6 units

10 units

16 units

which of the following choices is a possible length for DF? 17 39 19

divide 120 in the ratio of 1 : 4​

A band must pay a $2500 entrance fee, It will split the cost between its 25 members. How much will each member pay?
Please help quick

Inequality’s

c) Solve 3x + 7 > x + 19

Valerie is 30 inches tall and casts a shadow that is 12
inches long. At the same time, ber teddy bear casts a
shadow that is eight inches long. How tall is the teddy
bear?

WILL MARK YOU BRAINLIEST

A student wants to prove that she can solve a system of a system of equations by replacing one of the equations with two times that equation and adding the other equation. The original system was 12x +2y =30 and 10x+y = 26. The student claims that her first step is to add the two linear equations. Select the option that refutes the student claim

Andre drives a bike for 4 hours covering 160 km. Find the distance covered by him in 7 hours.

is this a real person ​