Transformations of Functions: Stretches, Compressions, and Reflections
In this lesson, we explore the transformations of functions through vertical and horizontal stretches and compressions. We will analyze how the parameters "a" and "k" in the functions y = af(x) and y = f(kx) affect the graph of f(x). When a > 1, the function f(x) is vertically stretched, while 0 < a < 1 indicates a vertical compression. For horizontal transformations, k > 1 compresses and 0 < k < 1 stretches f(x). We will graph and apply these transformations accurately, ensuring a comprehensive understanding of function transformations.
Transformations of Functions: Stretches, Compressions, and Reflections
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Presentation Transcript
Unit 1: Functions Minds On More Graphing!!!
Unit 1: Functions Minds On Graph the following functions: f(x) = x2 g(x) = 3f(x) h(x) = -g(x)
Unit 1: Functions Lesson 7: Stretches, Compressions, and Putting it all Together • Learning Goals: • I can vertically stretch and compress a function. • I can horizontally stretch and compress a function. • I can transform a function using translations, reflections, and stretch and compressions.
Unit 1: Functions Lesson 7: Stretches, Compressions, and Putting it all Together How does the value “a” in the function y = af(x) change the graph of f(x)? • When a > 1 f(x) is stretchedvertically by a factor of a • When 0 < a < 1, f(x) is compressedvertically by a factor a • AND • When a is negative, f(x) is ALSO reflected in the x-axis.
Unit 1: Functions Lesson 7: Stretches, Compressions, and Putting it all Together Let’s look at y = f(kx) WARNING! This “k” is not the same as k in y = a(x-h)2 + k
Unit 1: Functions Lesson 7: Stretches, Compressions, and Putting it all Together Graph the following functions: f(x) = x2 g(x) = f(3x)
Unit 1: Functions Lesson 7: Stretches, Compressions, and Putting it all Together How does the value “k” in the function y = f(kx) change the graph of f(x)? • When k > 1 f(x) is compressed horizontally by a factor of • When 0 < k < 1, f(x) is stretched horizontally by a factor of • AND • When k is negative, f(x) is ALSO reflected in the y-axis.
Unit 1: Functions Lesson 7: Stretches, Compressions, and Putting it all Together Given the graph of f(x), graph the indicated transformation
Unit 1: Functions Lesson 7: Stretches, Compressions, and Putting it all Together Given the graph of f(x), graph the indicated transformation
Unit 1: Functions Lesson 7: Stretches, Compressions, and Putting it all Together Given the graph of f(x), graph the indicated transformation
Unit 1: Functions Lesson 7: Stretches, Compressions, and Putting it all Together Graph the following function: f(x) = -
Unit 1: Functions Lesson 7: Stretches, Compressions, and Putting it all Together We need to apply transformations in a specific order: Reflections Stretches and/or compressions Translations
Unit 1: Functions Lesson 7: Stretches, Compressions, and Putting it all Together Given the graph of f(x), graph the indicated transformations
Unit 1: Functions Lesson 7: Stretches, Compressions, and Putting it all Together Given the graph of f(x), graph the indicated transformation
Unit 1: Functions Lesson 7: Stretches, Compressions, and Putting it all Together Given the graph of f(x), graph the indicated transformation
Unit 1: Functions Lesson 7: Stretches, Compressions, and Putting it all Together Given the graph of f(x), graph the indicated transformation
Unit 1: Functions Lesson 7: Stretches, Compressions, and Putting it all Together Given the graph of f(x), graph the indicated transformation
Unit 1: Functions Lesson 7: Stretches, Compressions, and Putting it all Together Sketch the graph of g(x)
Unit 1: Functions Lesson 7: Stretches, Compressions, and Putting it all Together • Homework • Page 102 #12 • Page 111 #9be • Page 120 #4ce • Page 129 #1, 2, 3, 4, 7
