# Domain of a function . Range of a function. Define ??

Jun 15, 2018

See explanation

#### Explanation:

Functions are typically written like so:

$y = f \left(x\right)$

...you have your input variable, x, and the function produces an output variable y from this.

The DOMAIN of the function is the set of all values that the input variable can have, for which the function is defined.

2 examples:

$y = 4 x$
$y = \frac{4}{x}$
...in the first function, the domain is all real numbers. The input variable x can take on any value from the set of all real numbers.
...in the second function, though, the domain is the set of all real numbers excluding zero. The input variable can't be zero, because the function isn't defined for x = 0, because you can't divide by zero.

The RANGE of a function is the set of all values that the output variable can take.

For example, if our function is $y = {x}^{2}$, then the RANGE of the function is the set of all real numbers greater than or equal to zero.
The Domain of this function is the set of all real numbers. So x can be negative, zero, or positive. Squaring these numbers gives a positive number, except for x = 0, in which case y = 0.