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.

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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.

Mathematics
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Graph 1
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Graph 2
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Graph 3
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Graph 4
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Graph 5
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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")
do you know how to find the vertical asymptotes ?
I am not sure how to do that. I was sadly not introduced throughly to the unit :(
http://www.purplemath.com/modules/asymtote.htm
Yeah I am not totally understanding how to relate that to finding domain and range i'm a bit confused
For the first one, \(f(x) = \dfrac{1}{x+1}\) take denominator =0, solve for x, what do you get?
knock knock!!! x +1 =0, x =??
ok! one moment
-1 ?
yes, domain relate to x, right? but you can't take x =-1 since it makes the function undefined, right? Hence D = \(\mathbb R/{-1}\)
So that would make the domain for the first graph undefined then?
How about the range? Look at the graph, y goes from -infinitive to +infinitive but at 0, Hence Range is \(\mathbb R/0\)
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
ahhhhhhhhhhhhh. That makes sense. I understand. I never understood the "all real numbers except.. ext."
i'm sorry, I do not understand the notation- by "R/0" you mean that the range is all real numbers but 0?
I only ask because I have to format it in sentence form
yup
it is not R/0. It is \(\mathbb R/\{0\}\). That the correct notation.
Yes. My computer would not let me copy that. That is what I meant
Would you mind helping me with the others?
what is the second function? \(f(x) = \dfrac{1}{x-2}+1\)??
x would equal 2 here. would this mean that the domain is all real numbers except for 2?
yup
and how would I find the range? i did not totally understand how you did that for the first graph
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|
for domain, you see that x goes from -infinitive to + infinitive except x =2|dw:1438655384625:dw|
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 \(\mathbb R/\{1\}\)
ok. I understand

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