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Chapter 1 1-1 Exploring Transformations

Chapter 1 1-1 Exploring Transformations. Warm-Up. Locate and label the following points in the graph A(3,2) B(-3,-5) C(0,-4) D(-1,4). Warm-up answers. A. C. D. B. Objectives. Students will be able to: Apply transformations to points and sets of points.

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Chapter 1 1-1 Exploring Transformations

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  1. Chapter 11-1 Exploring Transformations

  2. Warm-Up • Locate and label the following points in the graph • A(3,2) • B(-3,-5) • C(0,-4) • D(-1,4)

  3. Warm-up answers A C D B

  4. Objectives • Students will be able to: • Apply transformations to points and sets of points. • Interpret transformations of real world data.

  5. Exploring Transformation • What is a transformation? • A transformation is a change in the position,size,or shape of the figure. There are three types of transformations • translation or slide, is a transformation that moves each point in a figure the same distance in the same direction

  6. Translation • In translation there are two types: • Horizontal translation – each point shifts right or left by a number of units. The x-coordinate changes. • Vertical translation – each points shifts up or down by a number of units. The y-coordinate changes.

  7. Translations • Perform the given translations on the point A(1,-3).Give the coordinate of the translated point. • Example 1: • 2 units down • Example 2: • 3 units to the left and 2 units up Students do check it out A

  8. Translations • Lets see how we can translate functions. • Example 3: • Quadratic function • Lets translate 3 units up

  9. Translation • Example 4:Translate the following function 3 units to the left and 2 units up.

  10. Translation • Translated the following figure 3 units to the right and 2 units down.

  11. Reflection • A reflection is a transformation that flips figure across a line called the line of reflection. Each reflected point is the same distance from the line of reflection , but on the opposite of the line. • We have reflections across the y-axis, where each point flips across the y-axis, (-x, y). • We have reflections across the x-axis, where each point flips across the x-axis, (x,-y).

  12. Reflections • Example 1: • Point A(4,9) is reflected across the x-axis. Give the coordinates of point A’(reflective point). Then graph both points. • Answer : • (4,-9) flip the sign of y

  13. Reflections • Example 2: • Point X (-1,5) is reflected across the y-axis.Give the coordinate of X’(reflected point).Then graph both points. • Answer: • (1,5) flip the sign of x

  14. Reflection Example 3: Reflect the following figure across the y-axis

  15. Horizontal stretch/compress

  16. Vertical stretch/compress

  17. Stretching and compressing • Example 1: • Use a table to perform a horizontal stretch of the function y = f(x)by a factor of 4. Graph the function and the transformation on the same coordinate plane.

  18. Stretching and compressing • Example 2: • Use a table to perform a vertical compress of the function y = f(x)by a factor of 1/2. Graph the function and the transformation on the same coordinate plane.

  19. Student Practice • Practice B • Translations worksheet

  20. Homework • Page 11 • 2-10 and 14-16

  21. Closure • Today we learn about translations , reflections and how to compress or stretch a function. • Tomorrow we are going to learn about parent functions

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