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Math Help - I do not understand problmes 9 to 15 how do you determine domains and ranges again?

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    I do not understand problmes 9 to 15 how do you determine domains and ranges again?

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  2. #2
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    Let's look at 9 first:

    y=(x+1)^2-3

    A function's domain is all the possible x values that work within a function. A domain is often restricted by functions like \frac{x}{x-1}\where  x \neq 1 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 (-\infty,\infty)

    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 [-3, \infty)

    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.  y=x^3

    The domain will be (-\infty,\infty) and the range will also be (-\infty,\infty). 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.  y=\sqrt{x}

    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 [0,\infty), and that correspondingly, the range is also limited to [0,\infty).
    Last edited by RobLikesBrunch; August 27th 2009 at 02:21 PM.
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