chapter 1 1-1 exploring transformations
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
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Chapter 11-1 Exploring Transformations
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Warm-Up
• Locate and label the following points in the graph
• A(3,2)• B(-3,-5)• C(0,-4)• D(-1,4)
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Warm-up answers
A
B
CD
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Objectives
• Students will be able to:• Apply transformations to points and sets of
points.• Interpret transformations of real world data.
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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
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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.
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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 and2 units up
Students do check it out
A
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Translations
• Lets see how we can translate functions.• Example 3:• Quadratic function
• Lets translate 3 units up
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Translation
• Example 4:Translate the following function 3 units to the left and 2 units up.
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Translation
• Translated the following figure 3 units to the right and 2 units down.
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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).
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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
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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
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Reflection
Example 3:Reflect the following figure across the y-axis
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Horizontal stretch/compress
Horizontal Stretch or Compressf (ax) stretches/compresses f (x) horizontally
A horizontal stretching is the stretching of the graph away from the y-axis. A horizontal compression is the squeezing of the graph towards the y-axis. If the original (parent) function is y = f (x), the horizontal stretching or compressing of the function is the function f (ax).•if 0 < a < 1 (a fraction), the graph is stretched horizontally by a factorof a units.
•if a > 1, the graph is compressed horizontally by a factor of a units. •if a should be negative, the horizontal compression or horizontal stretching of the graph is followed by a reflection of the graph across the y-axis.
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Vertical stretch/compress
A vertical stretching is the stretching of the graph away from the x-axis.A vertical compression is the squeezing of the graph towards the x-axis. If the original (parent) function is y = f (x), the vertical stretching or compressing of the function is the function a f(x).•if 0 < a < 1 (a fraction), the graph is compressed vertically by a factorof a units. •if a > 1, the graph is stretched vertically by a factor of a units. •If a should be negative, then the vertical compression or vertical stretching of the graph is followed by a reflection across the x-axis.
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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.
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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.
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Student Practice
• Practice B• Translations worksheet
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Homework
• Page 11• 2-10 and 14-16
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Closure
• Today we learn about translations , reflections and how to compress or stretch a function.
• Tomorrow we are going to learn about parent functions