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Domain and range of a graphed function

by Grace Lim
(Jacksonville, FL, USA)

Please explain to me how to determine the domain and the range of a graphed function. They have it in the book, but it wasn't clear enough for my daughter. I wonder if you can explain it the way my daughter can understand. Thanks.

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May 28, 2010
Domain and Range of a Graphed Function
by: Karin

Thank you for submitting such a great question.

The domain of a function is always the x coordinate on a graph. The range of a function is always the y coordinate.

So, to give you an example, please view Example 2 on the following page: http://www.algebra-class.com/vertical-line-test.html

This is the graph of a quadratic function.

The domain of this function is: all real numbers. You can choose any number for x and substitute to find the corresponding y value. Therefore, the domain is open to any number that you choose.

The range of this function is: {y|y< 6} (Actually the symbol should be less than or equal to - I can't type this symbol).

Notice that the maximum point on this parabola is 6. Therefore, there is no y coordinate that is greater than 6. All of the points on this graph contain a y coordinate that is less than or equal to 6.

Now, I am not sure what course your daughter is taking. If she is taking a beginning Algebra course, they may not be getting this technical yet. If this is the case, then write down the ordered pairs for the points on the graph.

The domain contains the x coordinates of the ordered pairs, and the range contains the y coordinates of the ordered pairs.

I hope this helps you to better understand domain and range. Please let me know if you need further help.

All the best,
Karin

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