Absolute Value Functions

The absolute value function converts any real number, or the output of a variable expression, into its non-negative counterpart. We write this function using two vertical bars, also called the modulus symbol.

For the function f(x) equals the absolute value of x, the system operates using a two-part algebraic rule.

If an input is positive or zero, it remains unchanged, but negative inputs are multiplied by negative one, giving a positive output.

The domain of the absolute value function includes all real numbers, but its range is restricted to all non-negative real numbers. Plotting this function on the xy-plane creates a distinctive V-shaped plot.

This function can be used to monitor an assembly line, where a digital scale measures how far a package's weight deviates from its target weight of 10 kilograms. The deviation in weight will be the absolute value of x minus 10.

This gives the difference as a single positive value. If this difference exceeds the allowed tolerance of 0.2 kilograms, the package is either overfilled or underfilled, and the system instantly rejects the package.