Question

Can someone give me examples on how you'd write functions for the following transformations using function notation using variables:
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

Alright so say we have

f(x) = x

"translation of a units to the right and b units up "
to move a graph up or down....you add or subtract a number 'b here' to the function...

so f(x) = x + b

To move it left or right you add or subtract a number 'a here' from the 'x' in the function...so

f(x) = (x-a) + b

Answer 2

"reflection across the y-axis "

for this...if we still have f(x) = x

To reflect across the y-axis we need only put a '-' sign in front of the 'x' so it would be

f(x) = -x

Answer 3

"reflection across the x-axis"

For this

f(x) = x

We need to put the '-' sign in front of the function

-f(x) = x

and then simplify

Answer 4

Thank you.

Answer 5

Still need the other ones too?

Answer 6

Well just in case I'll post them :)

f(x) shifted upward a units = f(x) + a
f(x) shifted downward a units = f(x) – a
f(x) shifted left a units = f(x + a)
f(x) shifted right a units = f(x – a)
f(x) reflected about the x-axis = –f(x)
f(x) reflected about the y-axis = f(-x)
To rotate (A , B) 90 degrees counter clockwise -> (-B , A)
To rotate (A , B) 180 degrees counter clockwise -> (-A , -B)
To rotate (A , B) 270 degrees counter clockwise -> (B , -A)

Answer 7

Yeah. Thank you so much!!!

Answer 8

No problem! :)

Answer 9

For the rotations do you need to put "f(x) ="? o: