what is the range of x g(x)=(x+3)/(2x-4)

Do you have an idea about the domain. I realize that finding the domain is not the question.

yes the domain is all x not equal 2, but stuck with range

That's good because you can think of the domain as what goes into the function and the range as what comes out. The domain is the set of admissible values of x while the range is the set of possible values of y.

Looking at g(x)=(x+3)/(2x-4), I'm wondering if there is any value of y that is not possible to get out of this rational function.

What if x = 1/100. What would y be. The function looks as if it will not have big values. By talking about functional values, we are talking range.

I think you are right, the range is all the numbers - infinity to + infinity

do you think so?

just past this on google and see press enter g(x)=(x+3)/(2x-4)

Well, I'm not sure. I usually test a point or two. Let's look at the graph: http://www.wolframalpha.com/input/?i=%28x%2B3%29%2F%282x-4%29+%3D+y

Click there and let's see what the function is doing.

You see the vertical asymptote. That's a no cross vertical line where x = 2.

The large values of y will come as the function approaches x = 2 from the right. Do you see it climbing?

I really got confused :)

there is a gap on the graph but don't know what are the numbers

That is to be expected. Forget about the climbing. Turn your head sideways and look along the y-axis from top to bottom. Do you see any values of y that are missing. I'll draw a picture of that gap while you do that.

yes the are, I can see from 0 to 5

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