Question

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Answer 1

The domain of a function is the complete set of possible values of the independent variable.

In plain English, this definition means:

The domain is the set of all possible x-values which will make the function "work", and will output real y-values.

When finding the domain, remember:

• The denominator (bottom) of a fraction cannot be zero
• The number under a square root sign must be positive in this section

Example 1a

In the above attached attachment is the graph of `y = sqrt(x+4)`:

Domain: `x>=-4`

Interactive examples

Don't miss the applet exploring these examples here:

Domain and Range interactive applet

The domain of this function is `x ≥ −4`, since x cannot be less than ` −4`. To see why, try out some numbers less than `−4` (like ` −5` or ` −10`) and some more than `−4` (like ` −2` or `8`) in your calculator. The only ones that "work" and give us an answer are the ones greater than or equal to ` −4`. This will make the number under the square root positive.

Notes:

The enclosed (colored-in) circle on the point `(-4, 0)`. This indicates that the domain "starts" at this point.

We saw how to draw similar graphs in section 4, Graph of a Function. For a more advanced discussion, see also How to draw y^2 = x − 2.

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