Absolute value functions are functions that contain the absolute value of a variable expression. The graphs of absolute value functions often have a distinct V-shape with a vertex and are also often symmetric about their vertex.
The absolute value of a number is the non-negative value of that number.
The parent function of absolute value functions is the function f(x)=∣x∣. Other absolute value functions can be described as transformations of this parent function.
In this chapter, absolute value functions are graphed using a table of values. This is typically performed by finding a limited number of points on the graph and then use that the graphs display both symmetry and have a V-shape to draw the graph.
Their graphs of the absolute value functions are analyzed further by describing their key features. The key features include intercepts, increasing and decreasing intervals, minimum and maximum values, and the function's end behavior.
The effects of transformations on absolute value functions are explored in both the function rules and graphs of the functions. The transformations studied are vertical and horizontal translations. Reflections in the x- and the y-axis, and stretching and shrinking.
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