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Warm-up Find the value 1. k(x) = |x – 2|

Warm-up Find the value 1. k(x) = |x – 2| a. k ( –1) b. k( 0) c . k( 1) d . k( 2) e. k( 4) 2. f(x) = x² – 4 f( – 2) b. f( – 1) c . f( 0) d . f( 1) e. f( 2) 3. g(x) = |x + 4| – 3 g( – 7) b. g( – 4) c . g( –1) d . g( 0) e. g( 1)

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Warm-up Find the value 1. k(x) = |x – 2|

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  1. Warm-up Find the value 1. k(x) = |x – 2| a. k( –1) b. k( 0) c. k( 1) d.k( 2) e. k( 4) 2. f(x) = x² – 4 f( – 2) b. f( – 1) c. f( 0) d.f( 1) e. f( 2) 3. g(x) = |x + 4| – 3 g( – 7) b. g( – 4) c. g( –1) d.g( 0) e. g( 1) 4. h(x) = (x – 5)² – 9 h( 0) b. h( 2) c. h( 3) d.h( 5) e. h( 8)

  2. 1. k(x) = |x – 2| k( –1) b. k( 0) c. k( 1) d.k( 2) e. k( 4) |-1 – 2| = 3 |0 – 2| = 2 |1 – 2| = 1 |2 – 2| = 0 |4 – 2| = 2 2. f(x) = x² – 4 f( – 2) b. f( – 1) c. f( 0) (– 2)² – 4 = 0 (– 1)² – 4 = – 3 (0)² – 4 = – 4 d.f( 1) e. f( 2) (1)² – 4 = – 3 (2)² – 4 = 0 3. g(x) = |x + 4| – 3 g( – 7) b. g( – 4) c. g( –1) |-7 + 4| – 3 = 0 |-4 + 4| – 3 = –3 |-1 + 4| – 3 = 0 d.g( 0) e. g( 1) |0 + 4| – 3 = 1 |1 + 4| – 3 = 2 4. h(x) = (x – 5)² – 9 h( 0) b. h( 2) c. h( 3) (0 – 5)² – 9 = 16 (2 – 5)² – 9 = 0 (3 – 5)² – 9 = –5 d.h( 5) e. h( 8) (5 – 5)² – 9 = –9 (8 – 5)² – 9 = 0

  3. 8.1 Notes Handout

  4. In mathematics, changing or moving a figure is called a transformation. • Transformations that move a figure vertically, horizontally, or both are called translations. You can define the translation by simply adding to or subtracting from its coordinates. • The original figure is called the pre - image. The figure that results from a transformation is called the image. The figure’s points of the pre-image and image are called vertices.

  5. If we were using a graphing calculator • L1 would be the domain of the pre-image • L2would be the range of the pre-image • L3would be the domain of the image • L4would be the rangeof the image • When x is translated, the translation is described as translation left or right. • When y is translated, the translation is described as translationup or down .

  6. We can represent translations of figures in several ways: • Describe the transformation in words. • Using calculator lists. • Using ordered pair notation or equation • Table of the pre-image and image • Graph of the pre-image and image

  7. Example 1: • Translation right 12 units and down 10 units • L3 = L1 + 12, L4 = L2 – 10 • Pre-image is (x, y) and image is (x + 12, y – 10) • Table 5) Graph

  8. Example 2: a) List the vertices of the figure in the table below. b) Create the new vertices and graph the transformation of L3= L1 – 3 and L4 = L2 – 5. c) Describe the transformation. d) What is another way to write b)? Translation left 3 units and down 5 units Pre-image (x, y) image (x – 3, y – 5) A 5 2 A’ 2 – 3 B 3 4 B’ 0 – 1 C – 3 – 1 C ‘ – 6 – 6

  9. Example 3: • Graph quadrilateral ABCD with vertices A(5, 2), B(3, 4), C( – 3, – 1), D( – 1, – 3) b) Graph the translation right 3 units and up 5 units. c) Identify the vertices of A’ B’ C’ D’. d) Define the coordinates of any point of any points in the image using (x, y) as the coordinates of the original figure. (x + 3, y + 5) 5 + 3 = 8 2 + 5 = 7 3 + 3 = 6 4 + 5 = 9 -3 + 3 = 0 -1 + 5 = 4 -1 + 3 = 2 -3 + 5 = 2

  10. Linear function f(x) = x Domain is all Real Numbers Range is all Real Numbers Absolute value function f(x) = │x│ Domain is all Real Numbers Range y ≥ 0 Parent Graphs

  11. Quadratic Function f(x)= x² Domain: All real numbers Range: y ≥ 0 Cubic Function f(x)= x³ Domain: All real numbers Range: All real numbers

  12. Rational Function Domain: x ≠ 0 Range: y ≠ 0

  13. Square Root Function Domain: x ≥ 0 Range: y ≥ 0

  14. Assignment: Page 440 – 442 # 1 – 4 , 7, 10, and 11

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