Question 230520: what is the domain, range, and function of y=absolute value of x-3 +2
i put the domain as 3 and the range as 2 and the function as yes
Answer by rapaljer(4671)   (Show Source):
You can put this solution on YOUR website! It can be a great asset to be able to graph the function with a graphing calculator. However, a LOT of folks are NOT using graphing calculators so I'll show the regular way to do this.
y=|x-3| +2
First off, the domain in this is very easy. Ask yourself, "What values of x would be allowed in this formula?" Keep in mind that you are NEVER allowed to divide by ZERO, and if you have a square root or fourth root or something like that, then whatever is INSIDE the square root symbol MUST be GREATER THAN OR EQUAL TO ZERO! Those are the MAIN two restrictions you have to consider. Since there are NO denominators, and NO radicals, there are NO RESTRICTIONS, so ALL VALUES OF X are allowed. This means that Domain is ALL REAL VALUES OF X, or (-inf, inf).
To find the range is a bit harder. Do you realize that an absolute value graph is a V shaped graph, and this one opens UPWARD?? If so, then remember that RANGE means "What values of y will result if you substitute values of x into the function. In this case, it is a V shaped graph opening upward, and the SMALLEST value you could get for y would be 2. So Range is  .
Is it a function? Since every value of x that you plug into this function gives a UNIQUE value of y, the answer is YES! IT IS A FUNCTION.
If you need help Functions, Domain and Range, please see my own website for FREE non-traditional explanations of these very important topics. Do a "Bing" or "Google" search for my last name "Rapalje". Near the top of the search list, find "Rapalje Homepage", and near the top of my Homepage, look for the link "MATH IN LIVING COLOR." Choose "College Algebra", and look in "Chapter 2" for "Functions, Domain, and Range". My own students ALL thought my explanations were a LOT easier than the traditional explanations.
Also, I have TWO videos (they are free!) posted on my website on this topic. To see my videos (of me teaching my classes a few years ago!), from my Homepage, look for "Rapalje Videos in Living Color". Choose either Intermediate Algebra or College Algebra (depending upon your level of expertise!), and look for "Functions, Domain, and Range."
Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus
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