It is defined using three functions that were more comfortable with: x2 1, x 1, and the constant function. If we input 0, or a positive value, the output is the same as the input.į\left(x\right)=x\textx $10,000. The function g is a piecewise defined function. All of these definitions require the output to be greater than or equal to 0. It is the distance from 0 on the number line. Continuity of piecewise-defined functions This function is continuous everywhere, except possibly at x Since 6 is also the value of the function at x The. With a domain of all real numbers and a range of values greater than or equal to 0, absolute value can be defined as the magnitude, or modulus, of a real number value regardless of sign. For example, in the toolkit functions, we introduced the absolute value function f\left(x\right)=|x|. Piecewise Functions Piecewise Functions A Function Can be in Pieces We can create functions that behave differently based on the input (x) value. Sometimes, we come across a function that requires more than one formula in order to obtain the given output.
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