• Support PF! Buy your school textbooks, materials and every day products Here!

Range of rational function

  • Thread starter FlO-rida
  • Start date
  • #1
26
0
how can i find the range of a rational function

for ex. y=1/x+1
 
Last edited:

Answers and Replies

  • #2
jbunniii
Science Advisor
Homework Helper
Insights Author
Gold Member
3,394
179
What's the definition of the range of a function?
 
  • #3
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
33,154
4,838
Also, what exactly is your function? Most would interpret what you have written like so:
[tex]y = \frac{1}{x} + 1[/tex]

I suspect that what you really meant was this:
[tex]y = \frac{1}{x + 1} [/tex]

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
26
0
ok how would we find the range for that
 
  • #6
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
33,154
4,838
ok how would we find the range for that
The range for what? As I already said in post 4, it's not clear what you're working with.
 
  • #8
26
0
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:
  • #9
jbunniii
Science Advisor
Homework Helper
Insights Author
Gold Member
3,394
179
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.
[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

[tex]y = \frac{1}{x+1}[/tex]

What's the domain of this function?
 
  • #10
26
0
thats wat i mean i just didnt know how to do it
 
  • #11
26
0
y=\\frac{1}{x+3}
 
  • #12
jbunniii
Science Advisor
Homework Helper
Insights Author
Gold Member
3,394
179
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
26
0
[x]\neq[/-1]
 
  • #14
26
0
i just made an acc. yesterday
 
  • #15
jbunniii
Science Advisor
Homework Helper
Insights Author
Gold Member
3,394
179
OK, good. So let's consider two cases:

[tex]x < -1[/tex]

[tex]x > -1[/tex]

Start by focusing on the first case, so we're just considering [itex]x < -1[/itex]. For [itex]x[/itex] 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
26
0
it would go on to infinity, but wouldnt the range be expressed using y values
 
  • #17
jbunniii
Science Advisor
Homework Helper
Insights Author
Gold Member
3,394
179
it would go on to infinity, but wouldnt the range be expressed using y values
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 [itex]x < -1[/itex], then can y be positive at all?
 
  • #18
26
0
infinitely small
 
  • #19
26
0
so how would you express the range ({y|y...)
 
  • #20
jbunniii
Science Advisor
Homework Helper
Insights Author
Gold Member
3,394
179
infinitely small
OK, so you can make y as negative as you like by varying x over the interval [itex](-\infty, -1)[/itex]. How large can you make y if x is in the same interval?
 
  • #21
26
0
sorry i am still in math 20 and we didnt take interval notation yet
 
  • #22
jbunniii
Science Advisor
Homework Helper
Insights Author
Gold Member
3,394
179
sorry i am still in math 20 and we didnt take interval notation yet
No problem. It's just another way of writing

[tex]x < -1[/tex]

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
26
0
i think you can make it zero, but can you please explain
 
Last edited:
  • #24
jbunniii
Science Advisor
Homework Helper
Insights Author
Gold Member
3,394
179
  • #25
26
0
infinity? sorry but i just dont get this
 

Related Threads for: Range of rational function

  • Last Post
Replies
4
Views
1K
  • Last Post
Replies
8
Views
2K
  • Last Post
Replies
10
Views
3K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
5
Views
960
  • Last Post
Replies
4
Views
799
  • Last Post
Replies
8
Views
2K
Top