Expert: Michael Tadesse - 9/15/2009

Question
how do i tell if a problem is a function or not a function. also how do if ind the domian and range of a funciton

Answer
Hello Samantha

To tell whether a problem contains a function, it must contain an independent as well as dependent variables.
An independent Variable is a variable (with an unknown value) which can increase or decrease or even have any value without any limitation (regardless of the values of the dependent variable) provided that its values are in the domain of the function.

Dependent Variable: is a variable which always is dependent on the values of the independent variable. The Independent variable determines the dependent variable.

For example, y = x2

Observe this function carefully, Samantha.

You can substitute any real number in place of X. positive, negative or zero. But after the operation, the output is always non-negative. (Try it yourself, insert 1, -2, 5, 0 they result 1, 4, 25 and 0 respectively)

In this case X is the independent variable, on the other hand Y is the dependent variable restricted to non-negative numbers only.



To find the domain and range of a function is very simple but very crucial. So master it.

The Domain of a function is the region of some elements (numbers) which the function can take for its independent variable. It is a set of eligible numbers which the function can operate with.

For instance, 1/x, you can see that all real numbers are eligible but 0. You can’t divide any number by 0. So the domain of the function, 1/x is all real numbers with out 0.

The range of a function is the output of the operation in short.
After you inserted those eligible numbers you get a different result, different numbers. The collection of these numbers or results is called Range.

For example, √X, you know that you can put only non-negative numbers under the square root. The same is the result, you always get non-negative numbers including zero.
Therefore, the range of the function is the set of all non-negative numbers or
R ≥ 0 (All real numbers greater or equal to zero)