![]() If we input 0, or a positive value, the output is the same as the input.į\left(x\right)=x\textx $10,000. 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. 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|. You may specify the value of a free variable at any point in the equation, but only the first domain specification will be recognized.Sometimes, we come across a function that requires more than one formula in order to obtain the given output. Therefore, -5 is part of the interval from x-9 to x-5 in the above example. ![]() Consider the following piecewise function and we say f(t) is equal to and they tell us what its equal to based on what t is, so if t is less than or equal to -10, we use this case. Worked example: domain
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