absolute value function
f(x)=|x|
The absolute value function is a mathematical function that calculates the distance between a given number and zero on the number line, regardless of the direction (positive or negative) in which the number is located. It is typically denoted by | brackets around the input variable, such as |x|.
The absolute value function returns a non-negative value, since it only measures distance. Therefore, if the input is negative, the output is the positive equivalent of that value. For example, the absolute value of -4 is 4.
The absolute value function is used in a variety of mathematical contexts, such as solving absolute value equations and inequalities, finding the distance between two points in the coordinate plane, and calculating the magnitude of vectors in physics.
Graphically, the absolute value function is represented by a V-shaped graph, with the vertex at the origin and the arms extending upward and downward from there. The function is symmetric about the y-axis and has a slope of -1 to the left of the vertex and a slope of 1 to the right of the vertex.
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