What are the main transformations we can apply to a function?
There are several types of transformation of functions, being the most common: Reflection (vertical or horizontal) and Translation (vertical or horizontal).
What are the 5 transformations?
These lessons help GCSE/IGCSE Maths students learn about different types of Transformation: Translation, Reflection, Rotation and Enlargement.
How are the graphs of the functions obtained from the graph of f?
It is obtained from the graph of f(x) = x 2 1 by reflecting it in the x-axis. The graph of y = f (-x) is the graph of y = f (x) reflected about the y-axis.
Why do we transform functions?
A function transformation takes whatever is the basic function f (x) and then “transforms” it (or “translates” it), which is a fancy way of saying that you change the formula a bit and thereby move the graph around. This is three units higher than the basic quadratic, f (x) = x2. That is, x2 + 3 is f (x) + 3.
What transformation is needed to go from the graph of the basic function?
A vertical compression (or shrinking) is the squeezing of the graph toward the x-axis. if k > 1, the graph of y = k•f (x) is the graph of f (x) vertically stretched by multiplying each of its y-coordinates by k.
|Transformations of Function Graphs|
|-f (x)||reflect f (x) over the x-axis|
|f (x – k)||shift f (x) right k units|
Why are graph transformations important?
One useful and important technique in graph sketching is to consider transformation of functions. If you know the basic shape of a function, you can use that to work out what translations, reflections or stretches of that function will look like.