# Homework Help: Range of rational function

1. Mar 13, 2010

### FlO-rida

how can i find the range of a rational function

for ex. y=1/x+1

Last edited: Mar 13, 2010
2. Mar 13, 2010

### jbunniii

What's the definition of the range of a function?

3. Mar 14, 2010

### Angry Citizen

Think what "domain" and "range" are. What can "x" be, and what can "x" not be? With that in mind, what can "y" be and what can "y" not be?

4. Mar 14, 2010

### Staff: Mentor

Also, what exactly is your function? Most would interpret what you have written like so:
$$y = \frac{1}{x} + 1$$

I suspect that what you really meant was this:
$$y = \frac{1}{x + 1}$$

When you write a fraction on a single line, use parentheses. The second version above should be written this way: y = 1/(x + 1)

5. Mar 14, 2010

### FlO-rida

ok how would we find the range for that

6. Mar 14, 2010

### Angry Citizen

Do you know what domain and range are? Your instructor would not be giving you rational functions without a thorough treatment of the concepts of domain and range, and how they relate to rational functions.

7. Mar 14, 2010

### Staff: Mentor

The range for what? As I already said in post 4, it's not clear what you're working with.

8. Mar 14, 2010

### FlO-rida

the range for 1/(x+1) .the thing is that i am doing an assignment on rational functions that is ment to be completed without help from the teacher (it will be explained upon completion). i have already researched horizontal and vertical asymptote of rational functions, as well as the domain but i still cant find anything on how to express the range (not in interval notation). dont get me wrong i know what range is.

Last edited: Mar 14, 2010
9. Mar 14, 2010

### jbunniii

[EDIT] Weird, it was all garbled on my screen when I responded, but now it looks fine, both in my quoted version and in the original post!

OK, so the function of interest is

$$y = \frac{1}{x+1}$$

What's the domain of this function?

10. Mar 14, 2010

### FlO-rida

thats wat i mean i just didnt know how to do it

11. Mar 14, 2010

### FlO-rida

y=\\frac{1}{x+3}

12. Mar 14, 2010

### jbunniii

You can click on my equation (or any typeset equation on this site) and it will give you a pop-up window with the Latex code that produced it.

13. Mar 14, 2010

### FlO-rida

[x]\neq[/-1]

14. Mar 14, 2010

### FlO-rida

i just made an acc. yesterday

15. Mar 14, 2010

### jbunniii

OK, good. So let's consider two cases:

$$x < -1$$

$$x > -1$$

Start by focusing on the first case, so we're just considering $x < -1$. For $x$ in this range, can I make the function as big as I like? Can I make it as small as I like? If not, then what are some bounds? (Even if they're not the tightest possible bounds, it's a start.)

16. Mar 14, 2010

### FlO-rida

it would go on to infinity, but wouldnt the range be expressed using y values

17. Mar 14, 2010

### jbunniii

Yes, the range is expressed using y values.

What do you mean by "it would go on to infinity"? Can you make it infinitely large (positive)? Can you make it infinitely small (negative)?

If $x < -1$, then can y be positive at all?

18. Mar 14, 2010

### FlO-rida

infinitely small

19. Mar 14, 2010

### FlO-rida

so how would you express the range ({y|y...)

20. Mar 14, 2010

### jbunniii

OK, so you can make y as negative as you like by varying x over the interval $(-\infty, -1)$. How large can you make y if x is in the same interval?

21. Mar 14, 2010

### FlO-rida

sorry i am still in math 20 and we didnt take interval notation yet

22. Mar 14, 2010

### jbunniii

No problem. It's just another way of writing

$$x < -1$$

So how big can y get if x is in this interval? Can you make y be positive? Can you make y be zero?

23. Mar 14, 2010

### FlO-rida

i think you can make it zero, but can you please explain

Last edited: Mar 14, 2010
24. Mar 14, 2010

### jbunniii

What value of x causes y = 0?

25. Mar 14, 2010

### FlO-rida

infinity? sorry but i just dont get this