Did you know that some functions have big families?
Jenn, Founder Calcworkshop®, 15+ Years Experience (Licensed & Certified Teacher)
If you look around at all of your family members, there are certain traits or characteristics that you all have in common. It’s the genes that are passed down from generation to generation that help determine your eye color, hair color, height, etc., that help to display commonality among your family members.
Well the same thing can be said for functions!
How?
Graph of Quadratic Equation using Transformations
First we have to understanding how the basic or “mama” graph looks, then we can see how to transform or translate it by moving or shifting or stretching or reflecting this graph to create a diverse family. This process is called Graphing Using Transformations!
I like how Purple Math simplifies everything by saying, all we’re really doing is just changing the formula a bit; thereby moving the graph around.
Wait! Is this just like how we graphed Trigonometric Functions?
Yes! But instead of trig functions, we’re going to learn how to Graph Using Transformation for the following six families:
Graph of Cubic Equation using Transformations
- Lines
- Quadratics (Square)
- Cubics
- Absolute Value
- Square Root
- Cube Root
What’s so cool is that the process to graphing all six of these families is the same, just the shape changes! That means, all we have to do is learn what each part of the equation does, and how it effects the graph, and we can graph anything!
Likewise, if we can graph a function quickly, we can identify such things as domain and range, continuity, increasing and decreasing intervals, and even symmetry without too much effort.
Together we will walk through the building blocks for each of the families listed above with countless examples; seeing how each transformation effects its domain and range.
Transformations of Functions – Video
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