1. 1-1 Exploring Transformations
Chapter 1 section 1
1-1 Exploring Transformations

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

3. 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

4. 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.

5. 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

6. Translations Lets see how we can translate functions. Example 3:
Quadratic function
𝑦= 𝑥 2
Lets translate 3 units up

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

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

9. 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).

10. 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.

11. 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

12. 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

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

14. 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.

15. 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 y-axis.

16. 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.

17. Vertical/Horizontal stretch

18. Horizontal /vertical

19. 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.

20. 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.

21. 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.

22. Student practice
Problems 2-10 in your book page 11

23. Homework
Even numbers page 11

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