the problems are on here

http://www.montgomeryschoolsmd.org/S.../PreCalc09.pdf

- Aug 27th 2009, 12:46 PMyitsonggI do not understand problmes 9 to 15 how do you determine domains and ranges again?
the problems are on here

http://www.montgomeryschoolsmd.org/S.../PreCalc09.pdf - Aug 27th 2009, 12:54 PMRobLikesBrunch
Let's look at 9 first:

A function's domain is all the possible x values that work within a function. A domain is often restricted by functions like where because that would result in dividing by 0. I know this is a rather...imprecise definition, but I think we can work with it. The range is all the possible y values.

So looking here, is there an possible x value that won't work? No, there isn't. You could put any negative number as x or any positive number as x, and add one to it and square it without yielding an undefined answer. So the domain is simply the set of all real numbers or

In the range, on the other hand, we must look at all the possible resulting y-values. Notice that if we square something, the result will*always*be positive; so the lowest possible number that y can be is -3, which occurs when x = -1. However, as we know that the domain of x includes all real numbers, the (x+1)^2 part of the function can become infinitely large, mitigating the -3, such that y goes to infinity as x goes to infinity. This means that the range is simply

See if you can try the other problems from here. If you need more examples, go here: http://mathforum.org/library/drmath/...ain_range.html

Edit: I did some more for you:

10.

The domain will be and the range will also be . This is because you can cube any real number, so no x-value results in an undefined function, and the output of a cube results in the same sign as you started with (if you cube a negative, you get a negative), such that the entire spectrum of the real numbers can also be represented. You can see this with a graph of y=x^3: http://www.wolframalpha.com/input/?i=y%3Dx^3.

11.

We cannot find the square root of a negative number (as any number squared yields a positive number), so that means the domain of x is limited to the positive numbers. This means the domain is , and that correspondingly, the range is also limited to .