1-1 Exploring Transformations 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 Lets see how we can translate functions. Example 3: Quadratic function 𝑦= 𝑥 2 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 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 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