Download Section 1 - Juan Diego Academy

CHAPTER 1 SECTION 1
1-1 EXPLORING TRANSFORMATIONS
OBJECTIVES
• Students will be able to:
• Apply transformations to points and sets of points.
• Interpret transformations of real world data.
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
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.
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
TRANSLATIONS
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Lets see how we can translate functions.
Example 3:
Quadratic function
𝑦 = 𝑥2
Lets translate 3 units up
TRANSLATION
• Example 4:
Translate the following function 3 units to the left
and 2 units up.
TRANSLATION
• Translated the following figure 3 units to the right
and 2 units down.
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 side 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).
TRASFORMATIONS
• You can transform a function by transforming its
ordered pairs. When a function is translated or
reflected, the original graph and the graph of the
transformation are congruent because the size
and shape of the graphs are the same.
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
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
REFLECTION
Example 3:
Reflect the following figure across the y-axis
HORIZONTAL COMPRESS/STRETCH
• Imagine grasping two points on the graph of a
function that lie on opposite sides of the y-axis. If
you pull the points away from the y-axis, you
would create a horizontal stretch of the graph. If
you push the points towards the y-axis, you
would create a horizontal compression.
HORIZONTAL STRETCH/COMPRESS
Horizontal Stretch or Compress
f (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 factor
of 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 yaxis.
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 factor
of 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.
VERTICAL/HORIZONTAL STRETCH
HORIZONTAL /VERTICAL
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.
EXAMPLE
• Use a table to perform a horizontal stretch
of the function y = f(x) by a factor of 3.
Graph the function and the transformation
on the same coordinate plane.
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.
STUDENT PRACTICE
• Problems 2-10 in your book page 11
HOMEWORK
• Even numbers 14-24 page 11
CLOSURE
• Today we learn about translations , reflections and
how to compress or stretch a function.
• Tomorrow we are going to learn about parent
functions