Graphs of absolute value functions

The  exercise appears under the Algebra II Math Mission. This exercise recognizes the graphs of absolute value functions.

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


 * 1) Move the cards to the right graphs: This problem provides a collection of four graphs of absolute value functions. The student is expected to slide the algebraic expressions of the functions to the correct label for the graphs.Goavf1.png
 * 2) Draw the graph of the function: This problem provides a particular absolute value function. The student is asked to graph the function on a specified domain.Goavf2.png

Strategies
Knowledge of the parent function for absolute value function and the set of functional transformations 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 absolute value function generally looks like a letter V. It is composed of two lines with opposite slopes emanating from the same point, called the vertex.
 * 3) Adding and subtracting constants generally performs translations.
 * 4) Multiplying and dividing by constants generally performs compressions and stretches.
 * 5) Multiplying by negatives generally performs reflections.

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) Absolute value functions are useful for representing quantities that must always be positive, such as speed as opposed to velocity, or area and volume.