🧑Zayn Alazawi 📅June 27, 2020 📊Grade 11 Math
Today, we're going to explore the transformations of functions. Think of these transformations as the tools that allow us to alter the shape, position, and size of a function's graph. By the end of our session, you'll be able to confidently navigate through translations, reflections, stretches, and compressions.
I. Translations: Shifting the Landscape
Imagine a function graph as a piece of art on a canvas. Translations are like picking up that canvas and moving it around.
Vertical Translations:
Horizontal Translations:
II. Reflections: Flipping the Image
Reflections are like holding a mirror up to our function, changing its orientation.
Reflections across the x-axis:
Reflections across the y-axis:
III. Stretches and Compressions: Reshaping the Function
Stretches and compressions are like playing with a rubber band, altering the width or height of our function's graph.
Vertical Stretches/Compressions:
Horizontal Stretches/Compressions:
Vertical Translation:
Horizontal Translation:
Reflection across the x-axis:
Reflection across the y-axis:
Vertical Stretch:
Horizontal Compression:
Desmos Demo:
Click 'edit graph' to view the individual functions.
Apply a horizontal compression by a factor of 0.5 and a vertical translation of 3 units downward to the function \(f(x)=x^2\). Write down the transformed function and sketch its graph.
\(g(x)=0.5(x^ 2 )−3\)
Apply a sequence of transformations: a vertical compression by a factor of 0.3, a horizontal translation of 2 units to the left, and a reflection across the y-axis to the function \(f(x)=x^2\). Write down the transformed function and sketch its graph.
\(m(x)=−0.3(x+2)^2\)