Unit Activity: Introduction to Geometry and Transformations
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Transformations can be thought of as functions that take the points from one object (the pre-image) to the corresponding points
on another object (the image). In the unit, you saw examples of how algebra can be used to rewrite the coordinates of points after
they have been transformed. You can also use function notation to rewrite the coordinates. For example, these statements show
several different ways you can use function notation for the translation, T. of a point 6 units in the positive x direction:
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• T(x, y) = (x + 6,y)
• T:(x, y) = (x + 6,y)
• T<6,0>(x, y) = (x + 6,y)
• T6, O(x, y) = (x + 6,y)
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Part A
Write functions for each of 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 bunits up
• reflection across the y-axis
• reflection across the x-axis
• rotation of 90 degrees counterclockwise about the origin, point
• rotation of 180 degrees counterclockwise about the origin, point o
• rotation of 270 degrees counterclockwise about the origin, point o
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1. Translation: g(x) = f(x-a)+b.

2. Reflection around y-axis: h(x) = f(-x)

3. Reflection around x-axis: k(x) = -f(x)

4. Rotation of 90° :

5. Rotation of 180° : .

6. Rotation of 270° : .

Step-by-step explanation:

Let us assume that the transformations namely translation, reflection are applied to a function f(x) and the rotation is applied to the point ( x,y ).

So, according to the options:

We know that 'translation moves the image in horizontal and vertical direction'.

1. As we have to translate the function f(x) 'a' units to the right and 'b' units up. So, the new form of the function becomes g(x) = f(x-a)+b.

Further, we know that 'reflection means to flip the image around a line'.

2. As, we have to reflect the function f(x) around y-axis. The new form of the function is h(x) = f(-x).

3. As, we have to reflect the function f(x) around x-axis. The new form of the function is k(x) = -f(x).

Since, 'rotation turns the image around a point to a certain degree'.

4. As, we have to rotate ( x,y ) counter-clockwise to 90° about the origin, the new form of the function is .

5. As, we have to rotate ( x,y ) counter-clockwise to 180° about the origin, the new form of the function is .

6. As, we have to rotate ( x,y ) counter-clockwise to 270° about the origin, the new form of the function is .

answer: entity is prob the answer

step-by-step explanation:

see explanation

step-by-step explanation:

a

(6r + 7) + (13 + 7r) ( remove brackets and collect like terms )

= 6r + 7 + 13 + 7r

= 13r + 20

b

remove brackets and collect like terms

13 - r - 1 + r

= 12 - r

c

remove brackets and collect like terms

= - 8 - r + 2r - 4

= - 12 + r

d

remove brackets and collect like terms

= 7r - - - 6r

[-   - = - - = - ]

= r -