- #1

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how can i find the range of a rational function

for ex. y=1/x+1

for ex. y=1/x+1

Last edited:

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- #1

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how can i find the range of a rational function

for ex. y=1/x+1

for ex. y=1/x+1

Last edited:

- #2

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

- #3

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- #4

Mentor

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[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)

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ok how would we find the range for that

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- #7

Mentor

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The range for what? As I already said in post 4, it's not clear what you're working with.ok how would we find the range for that

- #8

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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 can't find anything on how to express the range (not in interval notation). don't get me wrong i know what range is.

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- #9

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[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

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

- #11

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

- #12

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[x]\neq[/-1]

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i just made an acc. yesterday

- #15

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[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

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it would go on to infinity, but wouldn't the range be expressed using y values

- #17

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it would go on to infinity, but wouldn't 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?

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infinitely small

- #19

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

- #20

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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

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

- #22

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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?

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

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- #24

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zero

What value of x causes y = 0?

- #25

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infinity? sorry but i just don't get this

- #26

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- #27

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That's right. You can make y as close to 0 as you like, but it never quite gets there. You can also make y as negative as you like.

So that means that for [itex]x < -1[/itex], the range of possible y values is [itex]y < 0[/itex].

Other ways of expressing the same thing are

[tex]\{y | y < 0\}[/tex]

or

[tex](-\infty,0)[/tex]

Now let's consider the other half of the domain: [itex]x > -1[/itex]. What range of y values are possible here?

- #28

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positve infinity or y > 0

- #29

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positve infinity or y > 0

OK, so if [itex]x > 1[/itex] then the possible range of y values is [itex]y > 0[/itex].

Now put the two halves together to get the total range of the function.

- #30

Science Advisor

Homework Helper

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In interval notation that would be [itex](-\infty, -1)\cup (-1, \infty)[/itex].

The "range" is the set of possible y values.

One way of finding the

For this simple function, you could also have thought, since a/b= 0 gives immediately a= 0 by multiplying both sides by b, "a fraction is 0 if and only if its numerator is 0". Here the numerator is the constant 1 which is never 0. y can never be 0.

- #31

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Thanks for the help, and just to be sure, the range is always expressed as y [tex]\neq[/tex] ...

- #32

Gold Member

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No, only sometimes, like here.

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