# quick questions!

• Sep 7th 2013, 09:44 AM
sakonpure6
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 :

Quote:

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?

Quote:

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?
• Sep 7th 2013, 10:44 AM
emakarov
Re: quick questions!
I am not sure I understand the question.

Quote:

Originally Posted by sakonpure6
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
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
can be represented by either a circle graph

What is a circle graph?

Quote:

Originally Posted by sakonpure6
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
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).