Graphing Radical Functions (just find domain and range.) Hi! I am working on the study of graphing radical functions. I have already graphed these functions, I just do not understand how to write domain&range for both. I have to write it in terms of "all real numbers" I will include all 5 graphs below. Would really appreciate help.

- anonymous

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- anonymous

Graph 1

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- anonymous

Graph 2

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- anonymous

Graph 3

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- anonymous

Graph 4

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- anonymous

Graph 5

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- anonymous

okay well basically you have to find the asymptote of each function and state that that's the only point that the function does not equal (e.g. all real numbers except"whatever x-intercept the asymptote is at")

- anonymous

do you know how to find the vertical asymptotes ?

- anonymous

I am not sure how to do that. I was sadly not introduced throughly to the unit :(

- anonymous

http://www.purplemath.com/modules/asymtote.htm

- anonymous

@Hero @pooja195 @triciaal

- anonymous

Yeah I am not totally understanding how to relate that to finding domain and range i'm a bit confused

- Loser66

For the first one, \(f(x) = \dfrac{1}{x+1}\)
take denominator =0, solve for x, what do you get?

- Loser66

knock knock!!! x +1 =0, x =??

- anonymous

ok! one moment

- anonymous

-1 ?

- Loser66

yes, domain relate to x, right? but you can't take x =-1 since it makes the function undefined, right?
Hence D = \(\mathbb R/{-1}\)

- anonymous

So that would make the domain for the first graph undefined then?

- Loser66

How about the range? Look at the graph, y goes from -infinitive to +infinitive but at 0,
Hence Range is \(\mathbb R/0\)

- Loser66

A little bit difference. domain is all numbers of x that make the function defined.
-1 makes the function undefined, hence domain is all real number BUT -1

- anonymous

ahhhhhhhhhhhhh. That makes sense. I understand. I never understood the "all real numbers except.. ext."

- anonymous

i'm sorry, I do not understand the notation- by "R/0" you mean that the range is all real numbers but 0?

- anonymous

I only ask because I have to format it in sentence form

- Loser66

yup

- Loser66

it is not R/0. It is \(\mathbb R/\{0\}\). That the correct notation.

- anonymous

Yes. My computer would not let me copy that. That is what I meant

- anonymous

Would you mind helping me with the others?

- Loser66

what is the second function? \(f(x) = \dfrac{1}{x-2}+1\)??

- anonymous

x would equal 2 here. would this mean that the domain is all real numbers except for 2?

- Loser66

yup

- anonymous

and how would I find the range? i did not totally understand how you did that for the first graph

- Loser66

to find the range of a radical function, you need asymptotes, that are the line the graph is never touch. like the graph of \(f(x) =\dfrac{1}{x-2}+1\)
it looks like |dw:1438655236291:dw|

- Loser66

for domain, you see that x goes from -infinitive to + infinitive except x =2|dw:1438655384625:dw|

- Loser66

for range, look at y-axis.|dw:1438655427018:dw|
the graph goes from -infinitive to +infinitive along y-axis but never have y =1, right?
hence range is \(\mathbb R/\{1\}\)

- anonymous

ok. I understand

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