Question

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

Answer 1

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

Answer 2

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

Answer 3

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.

Answer 4

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.

Answer 5

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.

Answer 6

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

Answer 7

do you think so?

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

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

Answer 13

I really got confused :)

Answer 14

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

Answer 15

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.

Answer 16

yes the are, I can see from 0 to 5