Domain and Range of a Function - 10/30/2014 Domain and...

10/30/2014 Domain and Range of a Function
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Domain and Range of a Function
Domain
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.
Remember:
The denominator (bottom) of a fraction cannot be zero
The number under a square root sign must be positive in this work
Example 1a
Here is the graph of
y
:
The domain of this function is
x
, since x cannot be less than . To see why, try out some numbers less
than (like or ) and some more than (like or ) in your calculator. The only ones that "work"
and give us an answer are the ones greater than or equal to . This will make the number under the square root
positive.
Notes:
1. The enclosed (colored-in) circle on the point . This indicates that the domain "starts" at this point.
2. 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 .
x

10/30/2014 Domain and Range of a Function
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Range
The range of a function is the complete set of all possible resulting values of the dependent variable ( y, usually),
after we have substituted the domain.
In plain English, the definition means:
The range is the resulting y- values we get after substituting all the possible x -values.
Tips
Substitute different x -values into the expression for y to see what is happening. (Ask yourself: Is y always
positive? Always negative? Or maybe not equal to certain values?)
Make sure you look for minimum and maximum values of y .
Draw a sketch! In math, it's very true that a picture is worth a thousand words.