![]() ![]() The range of a function is the set of values that can be produced by a function, while the domain of a function is the set of values that can. (A quotient of two polynomials is called a rational function. Ranges and domains are characteristics of functions. The Range is found after substituting the possible x- values to find the y-values. It depicts a relationship between an independent variable and a dependent variable. The domain is defined as the entire set of values possible for independent variables. A function is defined as the relation between a set of inputs and their outputs, where the input can have only one output i.e. Example 4.7.1 Find the domain and range of the following function: (f(x) 5x + 3 ) Solution. Domain and Range are the input and output values of a Function. The range of a function is the set of all possible output values of a function. The domain of a function is all possible values of x that can be used as input to the function, which will result in a real number as the output. We therefore say that the natural domain of the functions \(y=x+2\), \(y=3x^2-7\), \(y=\sin x\) and \(y=2^x\) is the set of all real numbers, denoted by \(\mathbb\). Definition: Domain and Range of a Function. For example, when we use the function notation f:R R f: R R, we mean that f f is a. In the function machine metaphor, the domain is the set of objects that the machine will accept as inputs. That is, we can substitute any \(x\)-value into the formula to obtain a unique \(y\)-value. The domain of a function is the set of its possible inputs, i.e., the set of input values where for which the function is defined. For the first four functions, we can take \(x\) to be any real number.
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