Piecewise Functions play by their own rules, but that doesn’t mean they have to be hard to handle.
Jenn, Founder Calcworkshop®, 15+ Years Experience (Licensed & Certified Teacher)
In fact, the key to understanding Piecewise-Defined Functions is to focus on their domain restrictions.
By simply dividing up the number-line or the coordinate plane into regions, or a “fence” as Cool Math calls it, we can quickly graph our function using our Transformation techniques for our Families of Graphs and find the domain and range.
It takes the sting right out of these prickly functions.
Jump Discontinuity
Moreover, we can see how Piecewise Functions can help us to establish rules for common step functions, such as the Greatest Integer Function.
The trick in graphing the Greatest Integer Function is to first understand that it looks like steps or a staircase, and that we are actually rounding down to the integer less than or equal to the value we plug in.
And with all of our knowledge of Graphing Using Transformations and Piecewise Functions, we are now able to discuss Symmetry.
Piecewise-Defined Function Example
There are countless types of symmetry, but the ones we want to focus on are
- X-axis Symmetry
- Y-axis (Even) Symmetry
- Origin (Odd) Symmetry
We will learn how to identify Symmetry given a graph and also how to determine whether a function is symmetric using algebraic techniques.
Together we will walk through every example in detail in order to ensure we have a solid foundation of both Piecewise Functions and Symmetry.
Graphing Piecewise Functions – Video
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