Chapter 11-1 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

B

CD

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 and2 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 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).

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 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.

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.

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

• Practice B• Translations worksheet

Homework

• Page 11• 2-10 and 14-16

Closure

• Today we learn about translations , reflections and how to compress or stretch a function.

• Tomorrow we are going to learn about parent functions