Question

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.

Answer 1

Graph 1

Answer 2

Graph 2

Answer 3

Graph 3

Answer 4

Graph 4

Answer 5

Graph 5

Answer 6

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")

Answer 7

do you know how to find the vertical asymptotes ?

Answer 8

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

Answer 9

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

Answer 10

@Hero @pooja195 @triciaal

Answer 11

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

Answer 12

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

Answer 13

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

Answer 14

ok! one moment

Answer 15

-1 ?

Answer 16

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

Answer 17

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

Answer 18

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

Answer 19

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

Answer 20

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

Answer 21

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

Answer 22

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

Answer 23

yup

Answer 24

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

Answer 25

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

Answer 26

Would you mind helping me with the others?

Answer 27

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

Answer 28

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

Answer 29

yup

Answer 30

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

Answer 31

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