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
1. f( x - a ) + b
2. g ( -x )
3. - h ( x )
4. R_{90}R
90
(x,y) = ( -y,x )
5.R_{180}R
180
(x,y) = ( -x,-y )
6.R_{270}R
270
(x,y) = ( y,-x )
Step-by-step explanation:
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,
Answer:
1. f( x - a ) + b
2. g ( -x )
3. - h ( x )
4. R_{90}R
90
(x,y) = ( -y,x )
5.R_{180}R
180
(x,y) = ( -x,-y )
6.R_{270}R
270
(x,y) = ( y,-x )
Step-by-step explanation:
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,