FUNCTION TRANSFORMATIONS

1
FUNCTION TRANSFORMATIONS

• I can translate linear and quadratic functions
  along a vector.
• I can reflect linear and quadratic functions
  across the x-axis, y-axis, y x or y -x.
• I can write the equation of a function after
  transformation.

2

• Graph y x2

x
y
Must plot a minimum of 5 points no
calculator!!!
3

• Graph y x2 3

x
y
Must plot a minimum of 5 points no
calculator!!!
4

• Graph y x2 1

x
y
Must plot a minimum of 5 points no
calculator!!!
5

• Graph y -x2

x
y
Must plot a minimum of 5 points no
calculator!!!
6

• Graph y -x2 1

x
y
Must plot a minimum of 5 points no
calculator!!!
7

• Reflect the function y x across the y-axis

New Equation
8

• Reflect the function y 2/3x -2 across the
  x-axis

New Equation
9

• Reflect the function y x2 2 across the x-axis

x
y
New Equation
10

• Reflect the function y -2x 1 across the line
  y x

11

• Reflect the function y x2 2 across the y x

x
y
12

• Translate the function y 3x 1 along lt-1,3gt

13

• Translate the function y x2 2 along lt2,-4gt

x
y
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COMPOSITIONS OF TRANSFORMATIONS

• I can perform a composition of two or more
  transformations.

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Compositions of Transformations

• Putting two or more transformations together
• ex Reflect across the y-axis, then
  rotate 90
• ORDER MATTERS

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Example 1B Drawing Compositions of Isometries
Draw the result of the composition of isometries.
?KLM has vertices K(4, 1), L(5, 2), and M(1,
4). Rotate ?KLM 180 about the origin and then
reflect it across the y-axis.
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Example 1B Continued
Step 1 The rotational image of (x, y) is (x,
y).
K(4, 1) ? K(4, 1), L(5, 2) ? L(5, 2), and
M(1, 4) ? M(1, 4).
Step 2 The reflection image of (x, y) is (x, y).

K(4, 1) ? K(4, 1), L(5, 2) ? L(5, 2), and
M(1, 4) ? M(1, 4).
Step 3 Graph the image and preimages.
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Check It Out! Example 1
?JKL has vertices J(1,2), K(4, 2), and L(3, 0).
Reflect ?JKL across the y-axis and then rotate it
180 about the origin.
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Check It Out! Example 1 Continued
Step 1 The reflection image of (x, y) is (x, y).

Step 2 The rotational image of (x, y) is (x,
y).
Step 3 Graph the image and preimages.
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Lesson Quiz
PQR has vertices P(5, 2), Q(1, 4), and P(3, 3).
1. Translate ?PQR along the vector lt2, 1gt and
then reflect it across the x-axis.
P(3, 1), Q(1, 3), R(5, 4)
2. Reflect ?PQR across the line y x and then
rotate it 90 about the origin.
P(5, 2), Q(1, 4), R(3, 3)