Domain and Range help!?

Posted on Mar 10, 2008 under domain news and reports | 533 Comments

Can someone please explain to me how to find the range and the domain of these functions. Also if you could please explain to me on how to find the range and domain that would be awesome! Thanks in advance for the help and sorry there is 4 problems any you can do would be a help.

{(0,2), (1,3), (3,4), (5,7)}
D=
R=

h(x)=4/5x-8
D=
R=

f(x)=|x|-3
D=
R=

f(x)=5/x+1
D=
R=

533 Responses to “Domain and Range help!?”

  1. laguna_beach101@sbcglobal.net Says:

    D: 0,1,3,5,
    R: 2,3,4,7

    see it goes in order. and a function is: a relation is a function if for every x there is exactly one y. so for example (-1,1) (2,0) (3,1) (3,2) (4,5) isn't a function. you can figure out the rest now maybe. i helped you with the first one.

  2. Domain = input = what values are you allowed to use for the variable in a function.

    Range = output = what possible values will a function spit out.

    Usually, a function is written in this way:

    f(x) = (some equation where x is a variable)

    Depending on the equation, or on the way you use the equation, there may be values of x that cannot be used or that the equation should be restricted to.

    For example, if the equation has a fraction with x in the denominator, then the denominator can never be zero.

    Example: h(x) = 4 / (5x-8), the bottom part is not allowed to be 0. Therefore x cannot be equal to 8/5.

    Any other number is OK. Therefore, the domain is all numbers except 8/5 (8/5 is not in the domain). You can use any number for the input (the value of x) except 8/5.

    These are all different ways of saying the same thing.

    — Range:

    Some functions will leave out possible answers. For example, the absolute value of a number can never be negative.

    Example: f(x) = |x|-3
    The domain can be any real number (including 0, or -pi or anything else).

    However, because |x| can never be less than 0, the output of f(x) can never be less than -3. Therefore the range is all numbers equal to or greater than -3. Range = [-3, +infinity)
    The square bracket shows that -3 does belong to the range. The round bracket shows that infinity is not part of the range (it is not a real number).

    The answer to that equation can never be less than -3, regardless of the input value used for x.

    These are all different ways of saying the same thing.

    The first one is special. Normally, when two values are given in that format (x, y), the first one is the input — from the domain — and the second one is the output — the range.

    It is actually the format (x, f(x)). The list of element (the four pairs) shows all possible cases. For each value of x, the list gives the value of f(x).

    Therefore, the domain consists of the four values that come first in each pair: {0, 1, 3, 5}
    The range consits of the four values that come second in each pair: {2, 3, 4, 7}
    You do not know what the equation is, but you know that any input chosen from the domain will give the corresponding value in the range.

    Things to watch for when determining the domain (the possible imput values) with real numbers.

    divisions: the denominator can never be zero.
    square roots: negative numbers do not have roots; however cube roots can be negative.
    Logarithms: cannot be negative AND cannot be zero.

    For real life problems, it depends on the situation. Let's say you are a navy meteorologist and you have developed an equation giving the temperature of the air (at some spot at some time) as a function of the height above the water.

    Then you would not use a negative value for height (even if the equation would still work) because an altitude of less than zero would put you under water (where there is no air). You would impose a limit on your domain even if the equation was able to handle negative numbers (in practice, you'd add a line in the computer program to prevent the input of negative numbers).

  3. hi!

    #1
    d = 0 1 3 4
    r = 2 3 4 7
    all the abscissa belongs to the domain and the ordinates to the range

    #2
    h(x) is also y
    y = 4/5x-8

    to get the domain, solve for y
    we already have the y in here

    since 5x – 8 is the denominator, it should not be zero so that the function will not be undefined
    so…
    5x – 8 ~ 0
    ~ means not equal to

    5x ~ 8
    x ~ 8/5
    domain: {x|x ~ 8/5}
    read as: x such that x must not be equal to 5

    to get the range, solve for x
    y = 4/5x-8
    5xy – 8y = 4
    y(5x – 8) = 4
    5x – 8 = 4/y
    5x = (4/y) + 8
    x = [(4/y) + 8] / 5

    range:
    y must not be equal to zero

    {y|y~0}

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