Transformations

The students should have learned and experienced the introduction to this concept in Math I class with positive and negative values for the functions.
 * __ Transformation Unit __**

The teacher may choose to conduct a brief review of the Math 1 concept with "building new functions from existing functions" to assess the students' level of comprehension of the topic. The teacher may take additional time to review activities to attempt to refresh the memory of the student.

The students will use their prior knowledge of linear transformations to build an understanding about transformations for quadratic and absolute value functions.

1- The students will be able to describe the difference between horizontal and vertical transformations ( meaning use of prior knowledge) a) Comparing and contrasting linear functions, quadratic functions and absolute values. b) Comparing vertical transformations to linear functions to Y intercepts, realizing the movement will be up and down. c) Extending the idea that the vertical shift will move any graph up and down. d) Understand the idea that a number inside the parenthesis are a horizontal shift and in the opposite direction. e) F notations inside the parenthesis will be horizontal movement on the graph and outside of the parenthesis is vertical shift.

The students will complete the activity with use of T charts, calculator and tables to complete the assigned functions and demonstrate an understanding.

__**Activity:**__ The students will use a graphing calculator to graph a function. The students then change the function data and then graph. 2- The students will be able to recognize the difference between stretches and shrinking with using a graph. (Further extension would be to use a graph with fixed points that need to be transformed like 2f(x) versus f(2x).) a) The students will compare and contrast from Secondary I graphing exponentials. b) The students will be able to demonstrate that a number larger than one will vertically stretch the graph while a number smaller then one will vertically shrink the graph. c) The students will be able to demonstrate that a number larger than one inside the parenthesis will horizontally shrink the graph ( anything contained within the parenthesis with x will do the opposite movement.) d) The students will be able to demonstrate that a number smaller than one inside the parenthesis will horizontally stretch the graph ( anything contained within the parenthesis with x will do the opposite movement.)

3- The students will be able to do a reflection over the x and y axis. a) The students will be able to demonstrate that -f(x) will be a reflection of the graph over the x axis.  b) The students will be able to demonstrate that f(-x) will be a reflection of the graph over the y axis.

4- The students will use a combination of horizontal and vertical translations, horizontal or vertical shrinks/stretches, reflections over the x and y axes or any combination to describe the set of equations and relate them to other functions. a)The students will create their own problems that will demonstrate these concepts. b) The students will write a story problem. They will share the information with another student and have the other student write the equation and solve the problem.