Graphs of nonlinear piecewise functions

The  exercise appears under the Algebra II Math Mission. This exercise practice finding the formula of a nonlinear piecewise function, given its graph.

Types of Problems
There is one type of problem in this exercise:


 * 1) Find the correct formula: This problem provides a graph of a nonlinear piecewise function. The student is asked to select the correct equation for the graph from the multiple choice list provided.Graphs of nonlinear piecewise functions.PNG

Strategies
Knowledge of writing domains and some of the parent graphs of common functions are encouraged to ensure success on this exercise. However, using a T-table is all that is necessary.
 * 1) One way to always create a graph is to create a T-table of values.
 * 2) An open dot is a whereas a closed dot indicates less than or equal or greater than or equal.
 * 3) Various functions can show up on this exercise, such as polynomials, conics and exponentials.
 * 4) Looking at the graph of the function $$y=f(x)$$, students should notice that it comes in two pieces.
 * 5) Students can come up with an equation for the piecewise function if they can come up with an equation for each piece of the function, and an interval over which each piece is defined.

Real-life Applications

 * 1) An ability to graph and recognize graphs quickly will increase proficiency in the calculus which studies rates of changes of functions.
 * 2) Square root functions are useful in physics when modeling curvature of certain geometric figures.