Final answer:
An absolute value function is characterized by its 'V' shaped graph, where the vertex is its minimum or maximum point. The function has linear pieces with a slope change at the vertex and is defined for all real numbers.
Step-by-step explanation:
Characteristics of an Absolute Value Function
An absolute value function is a mathematical expression that contains an absolute value operation. The characteristics of an absolute value function include:
- Its graph has a characteristic 'V' shape, which can open upwards or downwards depending on the sign in front of the absolute value expression.
- The vertex of the 'V' is the minimum or maximum point of the function, which occurs where the expression inside the absolute value is equal to zero.
- Absolute value functions have linear pieces with a change in slope occurring at the vertex.
- They are defined for all real numbers since absolute value is the distance from zero and all real numbers have a distance from zero.
- The function approaches its vertex in a linear fashion but never crosses the x-axis at a point other than the vertex unless transformed by additional terms.
For example, the absolute value function f(x) = |x| has a vertex at (0, 0) and consists of two linear pieces, one with a slope of 1 for x greater than 0, and one with a slope of -1 for x less than 0.