1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
makvit [3.9K]
3 years ago
15

Write functions for each of the following transformations using function notation. Choose a different letter to represent each f

unction. 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

please use this format:
T(x, y) = (x + 6, y)
T<6, 0>(x, y) = (x + 6, y)
T6, 0(x, y) = (x + 6, y)
Mathematics
1 answer:
kupik [55]3 years ago
6 0

Answer:

(a)\ T_{a,b} =(x +a,y+b)

(b)\ F_{y\ axis} = (-x,y)

(c)\ F_{x\ axis} = (x,-y)

(d)\ R_{o,90^o} = (-y,x)

(e)\ R_{o,180^o} = (-x,-y)

(f)\ R_{o,270^o} = (y,-x)

Step-by-step explanation:

Solving (a): Translate a units right, b units up

When a function is translated a units right, the number of units will be added to the x coordinate

When a function is translated b units up, the number of units will be added to the y coordinate.

So, we have:

T_{a,b} =(x +a,y+b)

Solving (b): Reflect across y-axis

When a function is translated across the y-axis, the x coordinate gets negated.

So, we have:

F_{y\ axis} = (-x,y)

Solving (c): Reflect across x-axis

When a function is translated across the x-axis, the y coordinate gets negated.

So, we have:

F_{x\ axis} = (x,-y)

Solving (d): 90 degrees rotation counterclockwise

When a function is rotated 90 degrees counterclockwise, the y-coordinates gets negated and then swapped with the x-coordinate.

So, we have:

R_{o,90^o} = (-y,x)

Solving (e): 180 degrees rotation counterclockwise

When a function is rotated 180 degrees counterclockwise, the coordinates are negated.

So, we have:

R_{o,180^o} = (-x,-y)

Solving (f): 270 degrees rotation counterclockwise

When a function is rotated 270 degrees counterclockwise, the x-coordinates gets negated and then swapped with the y-coordinate.

So, we have:

R_{o,270^o} = (y,-x)

You might be interested in
Sophia is saving money for a new bicycle. The bicycle will cost at least $623. Sophia makes $8.22 per hour.
Luda [366]
$8.22h greater than or equal to $623
3 0
3 years ago
Read 2 more answers
Find the area of the blue sector(s). The diameter is 14.
pav-90 [236]

The area of the entire circle is pi*(7)^2, or 49pi.


Due to the 90 degree angle, the area of the larger blue sector is


90

------- * 49 pi = 49/4 units^2

360


The area of the smaller blue sector is


48

------- 49 pi = (2/15)(49 pi) = 98 pi/15 units^2

360


The total area of the blue sectors is the sum of 98 pi/15 and 49 pi/4 (units^2):


59 units^2

5 0
3 years ago
Let f(x)=-6x+3 And g(x)=5x+4 Find F×G and state it's domain
a_sh-v [17]

Answer:b

Step-by-step explanation:

6 0
3 years ago
A number equals six less than four times a number. What is the number?
WITCHER [35]

Answer:

1.5

Step-by-step explanation:

set x = 6

and x less than four time of 6

it may mean 6÷4

6÷4 = 1.5 #

7 0
3 years ago
If you go out to eat, a good tip is $18 when the bill costs $100. What is this percent?
dlinn [17]

Answer:

This is a good tip and $18 is 18% of what the meal cost.

Step-by-step explanation:

On average the proper tip is 15% of the cost of your meal cost. In this case you have paid 18% of your meal cost.

4 0
3 years ago
Read 2 more answers
Other questions:
  • What is the value of x?<br><br> Enter your answer in the box.<br><br> x =
    13·2 answers
  • Suppose you have 15 days until your field trip and you need to raise $900 there are 10 students going on the field trip they wil
    14·1 answer
  • 30 points pls help image included
    8·1 answer
  • A 41 gram sample of a substance that's used to detect explosives has a k-value of 0.1392. Find the substance's half life, in day
    13·1 answer
  • Sketch a graph that has the following characteristics. (8 points: 2 points for each characteristic)
    11·2 answers
  • A seed company planted a floral mosaic of a national flag. The perimeter of the flag is 2,280 ft Determine the flag's width and
    13·2 answers
  • Give first the step you will use to seperate variable and then solve the equation:-<br>a) 4x=25​
    8·1 answer
  • If 20 kids were on abus ad 5got off to finger there holes how many kids are on the bus now
    15·2 answers
  • Write each phrase as a mathematical expression.
    10·1 answer
  • Can someone solve this?
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!