Absolute Value Functions

Definition

Absolute value functions are functions that represent the distance between a number and zero on a number line. They can be written as f(x) = |x|, where f(x) is the output (y-value) and x is the input (x-value).

Analogy

Think of absolute value functions as a mathematical "mirror" that reflects numbers across zero. Just like a mirror reflects your image symmetrically, an absolute value function reflects numbers symmetrically across the y-axis.

Related terms

Vertical Tangent Line: A vertical tangent line is a line that is perpendicular to the curve of a function at a specific point and has an undefined slope. It occurs when there is an abrupt change in direction or when the slope becomes infinite.

Smooth: In calculus, smooth refers to functions that are continuous and have no sharp corners or breaks in their graph. They exhibit gradual changes and have no abrupt changes in direction.

Piecewise Function: A piecewise function is made up of different equations defined for different intervals or pieces of the domain. It's like having multiple gears on a bike - each gear represents a different equation used to describe the function within its specific interval.