Results 1 to 4 of 4

Math Help - Graph/Domain/Range?

  1. #1
    Newbie
    Joined
    Dec 2007
    Posts
    14

    Graph/Domain/Range?

    I'm totally fried right now guys, I feel like I haven't seen equations like these in years!

    The domain of the function f(x)= 4-x is?

    The range of the function f(x)= 2- x^2 is?

    And finally...
    The graph of the function f(x)= 1/ (x^2-9):
    has two vertical asymptotes?
    is symmetric about the x axis but not about the y axis?
    has two horizontal asymptotes?
    is symmetric about the line x=3?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    10,063
    Thanks
    370
    Awards
    1
    Quote Originally Posted by lemon301 View Post
    I'm totally fried right now guys, I feel like I haven't seen equations like these in years!

    The domain of the function f(x)= 4-x is?

    The range of the function f(x)= 2- x^2 is?

    And finally...
    The graph of the function f(x)= 1/ (x^2-9):
    has two vertical asymptotes?
    is symmetric about the x axis but not about the y axis?
    has two horizontal asymptotes?
    is symmetric about the line x=3?
    Some definitions:

    The domain of a function is the set of possible values for the independent variable(s). In this case we are looking for the set of possible values for x. Generally it is easier to find what values of x are not possible, then give the answer as all real numbers not including the impossible values. So are there any values of x such that f(x) = 4 - x does not exist?

    The range of a function is a little more difficult. The range of a function is the set of values that the function returns. (ie. what values can f(x) take?) My best recommendation is to graph the function (which is a downward opening parabola) and see what values of the function are allowed. So is there a lower limit for what f(x) = 2 - x^2 can be? Is there an upper limit?

    For vertical asymptotes we are looking for values of x such that the denominator is 0.

    For horizontal asymptotes we are looking for what the behavior of the function is for x tending toward positive and negative infinity. If the function approximates a constant for these limits, then it has a horizontal asymptote.

    For symmetry about the x axis we are looking to see if for every point (x, f(x)) on the graph we also have the point (x, -f(x)) on the graph.

    For symmetry about the line x = 3, the simplest thing to do is first consider y = f(x - 3). This means translate the function three units to the left. Then the question becomes is f(x - 3) symmetric about the line x = 0, aka the y axis? If a function g(x) is symmetric about the y axis then g(-x) = g(x). So the question, in its final form, becomes: Is f(-(x - 3)) = f(x - 3)?

    Try your question with these and post what you come up with if you are still having problems.

    -Dan
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Dec 2007
    Posts
    14
    Quote Originally Posted by topsquark View Post
    Some definitions:

    The domain of a function is the set of possible values for the independent variable(s). In this case we are looking for the set of possible values for x. Generally it is easier to find what values of x are not possible, then give the answer as all real numbers not including the impossible values. So are there any values of x such that f(x) = 4 - x does not exist?

    The range of a function is a little more difficult. The range of a function is the set of values that the function returns. (ie. what values can f(x) take?) My best recommendation is to graph the function (which is a downward opening parabola) and see what values of the function are allowed. So is there a lower limit for what f(x) = 2 - x^2 can be? Is there an upper limit?

    For vertical asymptotes we are looking for values of x such that the denominator is 0.

    For horizontal asymptotes we are looking for what the behavior of the function is for x tending toward positive and negative infinity. If the function approximates a constant for these limits, then it has a horizontal asymptote.

    For symmetry about the x axis we are looking to see if for every point (x, f(x)) on the graph we also have the point (x, -f(x)) on the graph.

    For symmetry about the line x = 3, the simplest thing to do is first consider y = f(x - 3). This means translate the function three units to the left. Then the question becomes is f(x - 3) symmetric about the line x = 0, aka the y axis? If a function g(x) is symmetric about the y axis then g(-x) = g(x). So the question, in its final form, becomes: Is f(-(x - 3)) = f(x - 3)?

    Try your question with these and post what you come up with if you are still having problems.

    -Dan

    Thanks so much for the help! Only thing I'm having trouble with is domain. Right now I'm looking at an equation f(x)= [square root] 16 - x^2.
    I'm trying but I keep thinking different answers. I know it has to be [0,4] [-2,2] [0,16] or [-4,4]. I have the feeling if I keep trying I'm just going to come up with different answers lol.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    GAMMA Mathematics
    colby2152's Avatar
    Joined
    Nov 2007
    From
    Alexandria, VA
    Posts
    1,172
    Awards
    1
    Quote Originally Posted by lemon301 View Post
    Thanks so much for the help! Only thing I'm having trouble with is domain. Right now I'm looking at an equation f(x)= [square root] 16 - x^2.
    I'm trying but I keep thinking different answers. I know it has to be [0,4] [-2,2] [0,16] or [-4,4]. I have the feeling if I keep trying I'm just going to come up with different answers lol.
    It's domain is from -4 to 4. The radical cannot be negative, so solve for such an inequality...

    16 - x^2 \ge 0

    x^2 \le 16

    -4 \le x \le 4
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Domain and Range Help!
    Posted in the Calculus Forum
    Replies: 2
    Last Post: May 31st 2011, 11:43 AM
  2. Domain/Range of this e graph
    Posted in the Pre-Calculus Forum
    Replies: 6
    Last Post: December 15th 2010, 07:25 PM
  3. Replies: 6
    Last Post: September 16th 2009, 06:25 AM
  4. TI-nspire graph domain/range
    Posted in the Calculators Forum
    Replies: 0
    Last Post: January 9th 2009, 07:08 AM
  5. domain and range
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: September 30th 2008, 02:54 AM

Search Tags


/mathhelpforum @mathhelpforum