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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

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- Thread starter FlO-rida
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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?

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- #4

Mark44

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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

Mark44

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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 cant find anything on how to express the range (not in interval notation). dont 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!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.

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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- #13

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[x]\neq[/-1]

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i just made an acc. yesterday

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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.)

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

- #17

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

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infinitely small

- #19

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

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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?infinitely small

- #21

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

- #22

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No problem. It's just another way of writingsorry i am still in math 20 and we didnt take interval notation yet

[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

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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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What value of x causes y = 0?zero

- #25

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infinity? sorry but i just dont get this

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