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Math Help - quick questions!

  1. #1
    Senior Member sakonpure6's Avatar
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    quick questions!

    Hi, I just want to make sure of something, basically the question is asking to draw a translated function with the following properties :

    b)The range is {g(x)E R | 2<=g(x)<=4}
    can be represented by either a circle graph and a sinusoidal function (f(x)= sin x + 3) ? right? If so what is the equation for the circle graph?

    c)The domain is {x E R | x!=5}, and the range is {h(x) E R | h(x) != -3}.
    Answer can be either f(x)= 1/(x-5) + 3 and f(x) = -1(x-5) + 3 correct?
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  2. #2
    MHF Contributor
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    Re: quick questions!

    I am not sure I understand the question.

    Quote Originally Posted by sakonpure6 View Post
    the question is asking to draw a translated function
    Translated from what? After answering the question, it seems it should be a translation of very simple functions like sin(x) and 1/x.

    Quote Originally Posted by sakonpure6 View Post
    b)The range is {g(x)E R | 2<=g(x)<=4}
    The range of what: of g, which you need to create? If so, then this is a strange way to to say 2 ≤ g(x) ≤ 4. Claiming that {g(x) | x ∈ ℝ}, which is the range of g(x), coincides with {g(x) | x ∈ ℝ, 2 ≤ g(x) ≤ 4} is like saying, "My children are those of my children who are between the ages of 2 and 4" instead of simply "My children are between the ages of 2 and 4". Also, do you need just to draw the graph, as the question asks, or to come up with a formula?

    Quote Originally Posted by sakonpure6 View Post
    can be represented by either a circle graph
    What is a circle graph?

    Quote Originally Posted by sakonpure6 View Post
    and a sinusoidal function (f(x)= sin x + 3) ? right?
    Yes, for such f(x) we have 2 ≤ f(x) ≤ 4 for all x ∈ ℝ.

    Quote Originally Posted by sakonpure6 View Post
    c)The domain is {x E R | x!=5}, and the range is {h(x) E R | h(x) != -3}.

    Answer can be either f(x)= 1/(x-5) + 3 and f(x) = -1(x-5) + 3 correct?
    These functions do not take the values 3 instead of the required -3. And, of course, there are infinitely many other functions with these properties, but they may need to be given by more complex (e.g., piecewise) definitions. Finally, if h is indeed the intended name for a new function and not something that was defined earlier, then you probably should call the function h(x) and not f(x).
    Thanks from sakonpure6
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