Graphs of piecewise linear functions

The  exercise appears under the Algebra II Math Mission. This exercise recognizes the graphs of piecewise linear functions.

Types of Problems
There are three types of problems in this exercise:


 * 1) Draw the graph of the function: This problem provides a particular piece-wise function composed solely of linear pieces. The student is asked to graph the function on a specified domains.Gopwlf1.png
 * 2) Determine the intervals in interval notation: This problem provides a graph that is piece-wise linear and defined on several intervals. The student is asked to represent the intervals using standard interval notation.Gopwlf2.png
 * 3) Determine the intervals using less than vs. less than or equal to: This problem provides a graph that is piece-wise linear and defined on several intervals. The student is asked to represent the intervals by choosing appropriate symbols from a collection of drop-down lists.Gopwlf3.png

Strategies
Knowledge of the interval notation for domain and graphing lines 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) A linear function can be constructed by only graphing the endpoints.
 * 3) The endpoints of the functions on this exercise always appear at integer coordinates.
 * 4) An open dot is less than and is represented by a parentheses, a closed dot is less than or equal to and is represented by a bracket.

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) Piece-wise functions occur frequently in business for plans with varying prices. For example, phone plans or riding in a taxicab.