Domain and Range
Date: 08/25/97 at 12:50:17 From: Jenni Subject: Pre-Cal Hi. I'm a junior in high school and I need help with my pre-cal. I don't understand what we are doing in class. Can you explain about Domain and Range? I don't get it. I also have problems with Piecewise Function, Notation, Boolean Test, Transformation on Fraction, Operation on Function, Compositions of functions, and domain of composite. Thanks.
Date: 08/25/97 at 13:36:18 From: Doctor Ken Subject: Re: Pre-Cal Hi Jenni - The basic concept of domain and range is pretty simple. Here are the facts: - The domain of a function is the set of all the stuff you can plug into the function. - The range of a function is the set of all the stuff you can get out of the function. Let's do an example: f(x) = x^2 (that's x squared) What's the domain? Well, you can plug any old real number you want into this function: I can square 4, or -7, 1.01738, or whatever, and the world doesn't blow up. What's the range? Well, let's think about it. If I plug any number into this function, am I ever going to be able to get a negative number out of it? Nope! (Unless you're dealing with imaginary numbers, and I bet you're not!) So it looks like the range of this function is the set of all non-negative numbers (the positive numbers plus zero). And in fact, that's the right answer. Let's try another example: f(x) = 1/(x-5). What numbers can we plug into this function? Well, it looks like any number will do. But wait! What happens if we plug in 5? We divide by zero, and the world blows up. So let's not plug in 5. Since any other number is fine, the domain of this function is: all real numbers except 5. What's the range? I'll leave that one to you. Here's an anonymous tip. In general, when you're trying to find the domain of a function, there are two things you should look out for. They are: (1) Look for potential division by zero. (2) Look for places where you might take the square root of a negative number. Since these are the two easiest ways to make the world blow up, these are the things you really have to watch out for. For your other questions, you can look around in the calculus and pre-calculus pages in our archives. Two good pages to start looking at are High School Calculus http://mathforum.org/library/drmath/sets/high_calculus.html High School Functions http://mathforum.org/library/drmath/sets/high_functions.html There's lots of good stuff there. Good luck with it! -Doctor Ken, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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