1. Unit 4: Functions, Relations, and Transformations

2. Unit Objectives. Interpret graphs of functions and relations Review function notation. Learn about the linear quadratic, square root, absolute-value families of functions. Apply transformation-translation, reflection, and dilations to the graphs of functions. Transform functions to model real-world data.

3. October 16, 2015 Objectives: 1.Interpret graphs of real-world functions. 2.Identify the maximum and minimum of graphs. 3.Given a real-world situation make a graphical interpretation. Warm-up. Factor the following:

7. Sketch a graph that shows the relationship of time as the independent variable to the height of the fluid in the beaker as the dependent variable. Show your work on the white board. a. b. c.

9. October 22, 2015 Objectives: 1.Students will define a function in terms of the relationship between the independent and dependent variables. 2.Students will apply function notation and review the vertical line test. 3.Define the domain and range of a function.

10. What is a function?

11. Function definition Function : A relationship for which every value for the independent (x) variable has at most one value of the dependent (y) variable.

12. Function f is defined by the equation and function g is defined by the graph below:

13. Which is a function? A. B. C.

14. Which is a function? A. B. C.

15. Which is a function? a. b. c.

16. Use the functions to find the values:

17. October 23, 2015 Objectives: 1.Explore what happens to the equation of a line when you translate the line. 2.Learn how to write an equation that translates a function horizontally h units and vertically k units. 3.Describe the graph of an equation in the form by relating it to the graph of.

19. After the quiz. On your calculator graph the following:

20. Warm-Up On your calculator graph the following:

22. October 26, 2015 Objectives: 1. Explore the horizontal and vertical shifts of a function.

25. A. How does the graph of compare with the graph of B.The graph of the line is translated right 4 units and down 5 units. Write an equation of the new line.

27. Exit Question: From the function write the translation as shown in red.

28. October 27, 2015 Objectives: 1. Examine the graph of 2.Find equations for translation of the graph Warm-up: find the x-intercepts of the quadratic equation. This means; solve for x when y = 0.

29. In this lesson you will experiment with translation of the graph of the function. The special shape of this graph is called a parabola. Parabolas always have a line of symmetry that passes through the parabola’s vertex.

31. October 28/29, 2015 Objectives: 1.Demonstrate the transformation of a quadratic equation using the N-spire. 2.Graph the square root function and demonstrate it’s transformations. 3.Introduce reflection of a function using the square root function. Warm-up: Handout, groups of two.

34. TI- Nspire Navigator exercise. 1.Log onto Schoolapaloza network on your N- spire. 2.User name is; first initial and last name with no spaces. 3.ID is your school ID.

37. Reflection of a Function: A reflection is a transformation that flips a graph across a line, creating a mirror image. Given the graph of y = f(x): 1.The graph of y = f(-x) is a horizontal reflection across the y-axis. 2.The graph of y =- f(x) is a vertical reflection across the x-axis.

40. October 30, 2015 Objectives: 1. Reflection practice. Warm-up. Use the formula for the partial sum of geometric series: to find the sum of 3 + 6 + 12 + 24 + …. + 1536, where

45. November 5, 2015 Objectives: 1.Understand how to apply dilation to a function (vertical and horizontal stretch) 2.Identify the scale factor of a dilated graph. Dilation Scale factor Stretch Rigid transformation Non-rigid transformation Warm – Up: Graph

54. Section 4.6 Notes

56. November 6, 2015 Objectives: 1.Describe two ways to tell if a graph is a rigid transformation of a parent function. 2.Apply the rules for the dilation, reflection and transformation of a function. Warm-Up Sketch the following: A quadratic function that is reflected over the x-axis, vertically dilated by a factor of 3 and horizontally dilated by a factor of 2. And transformed 5 units to the left and 4 units up.

58. Exit Slip Nov. 4/5

59. 1.

60. 2.

61. 3.

62. 4.

63. December 3, 2014 Objectives: 1.More on Dilation of functions

64. Page 226, problems 2, 3

65. Page 227, problem 7

66. December 10, 2014 Objectives: Students will brainstorm the big ideas of the first semester units. 1.Recursive Sequence. 2.Linear Systems 3.Statistics 4.Transformation of Functions.

67. Each table will be assigned one of the first semester units. Your table will be given 10 minutes to write down as much information about that unit. Such as: big ideas, terms, examples ect. Remember you are up against at least one other table. Let’s see who does a better job.