Functions and Families

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Unit 3 Functions and Families Name: Date: Hour: Function Transformations Notes PART 1 By the end of this lesson, you will be able to Describe horizontal translations and vertical stretches/shrinks of

1 Unit 3 Functions and Families Name: Date: Hour: Function Transformations Notes PART 1 By the end of this lesson, you will be able to Describe horizontal translations and vertical stretches/shrinks of functions Graph horizontally translated and vertically stretched/shrunk functions Write equations of functions given the horizontal translations and vertical stretches/shrinks Transformations: Horizontal Translation: What do Horizontal Translations Look Like with Each Parent Function? Function Linear y = x Quadratic y = x 2 Square Root y = x Absolute Value y = x Horizontal Translation LEFT Horizontal Translation RIGHT Example 1: a. Identify and graph the parent function f(x) = x 2. b. Graph the translated function f(x) = (x + 1) 2.

2 Example 2: a. Identify and graph the parent function f(x) = x b. Write the equation of the graph that is translated right 2 units. c. Graph it. Example 3: a. Identify and graph the parent function f(x) = x b. Graph the translated function f(x) = (x 1) Vertical Stretch/Shrink: What do Vertical Stretches/Shrinks Look Like with Each Parent Function? Function Linear y = x Quadratic y = x 2 Square Root y = x Absolute Value y = x Vertical STRETCH Vertical SHRINK Example 4: a. Identify and graph the parent function f(x) = x. b. Graph the translated function f(x) = 3x. 2

3 Example 5: a. Identify and graph the parent function f(x) = x b. Write the equation for the function that vertically shrinks by 2 units. c. Graph it. Example 6: a. Identify and graph the parent function f(x) = x b. Graph the translated function f(x) = 2 x Example 7: Now, using your graphing calculator to help, explain how each transformed function has moved from the parent function of f(x) = x 2. REMEMBER: ORDER MATTERS! a. f(x) = 3(x 2) 2 b. f(x) = 1 (x + 1)2 3 c. f(x) = 4(x + 4) 2 Example 8: Now, let s go the other way. Each function described is the graph of f(x) = x. Write an equation for each function. a. The function is translated left 3 units. b. The function is translated right 5 units and vertically stretched by 2 units. c. The function is translated right 1 unit and vertically shrinks by 3 units. d. The function is translated left 8 units and vertically shrinks by 5 units. 3

4 Quick Check Function Transformations PART 1 1. Identify the transformations taking place from the parent function f(x) = x. Then graph the transformed function. g(x) = 3 x 2 2. Write an equation that represents the following transformations of the parent function f(x) = x 2 Translated left 3 units and vertically shrinks by 7 units. Self-Assessment Learning Goals Describe horizontal translations and vertical stretches/shrinks of functions Graph horizontally translated and vertically stretched/shrunk functions I am unsure of or confused about this I am ready to start practicing I am already good at this Write equations of functions given the horizontal translations and vertical stretches/shrinks My Goals for Today- thinking about what I am good at, where am I confused and what do I need to work on? What do I do if I am confused or need to work on a learning target? 4

5 Unit 3 Functions and Families Function Transformations Notes PART 2 By the end of this lesson, you will be able to Describe reflections and vertical translations of functions Graph reflected and vertically translated functions Write equations of functions given the reflections and vertical translations Reflection: What do Reflections over the X and Y Axis Look Like with Each Parent Function? Function Linear y = x Quadratic y = x 2 Square Root y = x Absolute Value y = x Reflection over the X-AXIS Reflection over the Y-AXIS Example 1: a. Identify and graph the parent function f(x) = x 2. b. Graph the translated function f(x) = x 2. Example 2: a. Identify and graph the parent function f(x) = x b. Write the equation for the function that is reflected over the y-axis. c. Graph it. 5

6 Example 3: a. Identify and graph the parent function f(x) = x b. Graph the translated function f(x) = ( x) c. Describe the transformations. Vertical Translation: What do Vertical Translations Look Like with Each Parent Function? Function Linear y = x Quadratic y = x 2 Square Root y = x Absolute Value y = x Vertical Translation UP Vertical Translation DOWN Example 4: a. Identify and graph the parent function f(x) = x. b. Graph the translated function f(x) = x 4. Example 5: a. Identify and graph the parent function f(x) = x b. Write the equation for the function that is translated down 2 units. c. Graph it. 6

7 Example 6: a. Identify and graph the parent function f(x) = x b. Graph the translated function f(x) = x + 1 Putting it All Together H What does it Look Like? Example S R V Example 7: Now, using your graphing calculator to help, a. Identify the parent function and b. describe the transformations. REMEMBER: ORDER MATTERS! a. f(x) = 2 x b. f(x) = 1 3 x 1 c. f(x) = 4(x + 2)

8 Example 8: Now, let s go the other way. Write an equation for each function described. a. Transform the function y = x 2 : Translate right 3 units, stretch vertically by 2 units, reflect over the x-axis, and translate down 2 units. b. Transform the function y = x: Translate left 2 units, vertically shrink by 2, and reflect over the x-axis. c. Transform the function y = x: Vertically shrink by 4, reflect over the x-axis, reflect over the y-axis, and translate up 4 units. d. Transform the function y = x : Vertically stretch by 2, reflect over the y-axis, translate down 3 units. Quick Check Function Transformations PART 2 1. Identify the transformations taking place from the parent function f(x) = x. Then graph the transformed function. g(x) = 3 x Write an equation that represents the following transformations of the parent function f(x) = x 2. Translated left 3 units, vertically shrinks by 7 units, reflect over the x-axis, and translated up 5. Learning Goals Self-Assessment I am unsure of or confused about this I am ready to start practicing I am already good at this Describe reflections and vertical translations of functions Graph reflected and vertically translated functions Write equations of functions given the reflections and vertical translations My Goals for Today- thinking about what I am good at, where am I confused and what do I need to work on? What do I do if I am confused or need to work on a learning target? 8

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Section 1.6 & 1.7 Parent Functions and Transformations

Math 150 c Lynch 1 of 8 Section 1.6 & 1.7 Parent Functions and Transformations Piecewise Functions Example 1. Graph the following piecewise functions. 2x + 3 if x < 0 (a) f(x) = x if x 0 1 2 (b) f(x) =