1 - 1 E X P LO R I N G T RA N S F O R M AT I O N S

CHAPTER 1 SECTION 1

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

• Lets see how we can translate functions.• Example 3:• Quadratic function

• 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 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.

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.

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