Question

please help me]

Explain what domain and range are, Under what circumstances will a function have domain other than all real numbers? Provide an example of a function whose domain is all real numbers and explain why. Your example can be either a graph or an equation. Provide an example of a function whose domain isn't all real numbers and explain why. Your example can be either a graph or an equation. Provide a third example to find the domain of.

Answer 1

Domain: the set of possible values of the independent variable or variables of a function
Range: the set of values that a given function can take as its argument varies.

A function will have a domain other than the set of all real numbers when the substitution of at least one real number into the function will result in either an unsolvable statement, or allow for there to be input(s) with more than one output.

The domain of y = x is the set of all real numbers because no matter what the input, there will always be a real and singular output. (The graph of this function is a line through the origin with a slope of 1.)

The domain of \[y=\sqrt{x}\] is all positive numbers and zero, because the input of a negative number would result in an unsolvable statement. Its domain is therefore not the set of all real numbers. (The graph of this function is a slowly growing curve in Quadrant I.)

3rd Example: \[y = \frac{ 10 }{ x }\] The domain of this example is all real numbers except zero, since one cannot divide by 0.