Question

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

Answer 1

@amorfide

Answer 2

• translation of a units to the right and b units up
this means you are going A in the positive x direction
so if I had f(x)=x
translating a in the positive X direction means I get F(x+a)= (x-a)
translating b units up means you are going b in the positive Y direction
so if I had
f(x)=x
f(x)+b = x+b

so to get translation a in positive x and b in positive y I get
f(x)=x
f(x+a)+b=(x-a)+b
• reflection across the y-axis

to reflect a function across the y axis
f(x)=x
f(-x)=(-x)
• reflection across the x-axis

reflection across x axis
f(x)=x
-f(x)= -(x)

Answer 3

I don't know how to describe rotations

Answer 4

@pooja195

Answer 5

@TheSmartOne

Answer 6

@amorfide thank you so much, you're a life saver. I just need to answer 1 more and i'm finished with my entire online class lol

Answer 7

@amorfide c. In the same way that other functions can be combined, a series of transformations can be combined into a single function. For example, this statement for the function S shows one way to represent the rotation of a point 270° counterclockwise about the origin followed by a translation 3 units to the left and 1 unit up: S(270, O)/<-3,1>(x, y) = (y – 3, -x + 1).

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 8

I can not do rotations I am sorry post this as a question and hope someone comes along

Answer 9

@amorfide its fine but thank you so much !

Answer 10

np I try to help :)