SOLUTION: Under what circumstances would the domain be something other than all real numbers? Provide an example.

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Question 614727: Under what circumstances would the domain be something other than all real numbers? Provide an example.
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
For functions in which there are NO DENOMINATORS and NO SQUARE ROOTS, the DOMAIN is ALL REAL NUMBERS. An example would be y=x^2.

However, if you have a variable in a DENOMINATOR, like y=3%2F%28x-5%29, then the domain is all values of x except x=5.

If you have a square root, like y=sqrt%28x-5%29, then there is a restriction that the radicand, which is x-5, must be greater than or equal to zero. That is, x-5%3E=0. This means x%3E=5. I have a similar explanation with more details on my website.

You might want to see my own NON-TRADITIONAL explanation of FUNCTIONS, DOMAIN, and RANGE on my own website. To find my website, use the easy-to-spell and easy-to-remember link www.mathinlivingcolor.com. This link takes you to a single page with a single link near the bottom of the page. Click on this link, and it takes you to my Homepage.

Once you are on my Homepage, look for "Basic, Intermediate, and College Algebra: One Step at a Time." Choose "Intermediate or College Algebra", and look in "Chapter 5" for Intermediate Algebra, and Chapter 2 for College Algebra. Then, the hardest of the problems in these sections are solved IN COLOR on the Math in Living Color page for the respective sections.

On the topic of Functions, Domain and Range, I also have VIDEOS of me teaching this topic a few years before I retired. To find the videos, look on my Homepage for "Rapalje Videos in Living Color." Look in Intermediate or College Algebra respectively for the video on Functions, Domain, and Range. The videos, like everything else on my website, are all FREE!!! Check it out!! Math is usually not as hard as it looks if you get a decent explanation of it!!

I hope this is helpful. For ANYONE interested in using my FREE website for ANY TOPIC in math, just send me an Email at rapaljer@seminolestate.edu.

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus