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anonymous

  • one year ago

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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  1. anonymous
    • one year ago
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    Graph 1

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  2. anonymous
    • one year ago
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    Graph 2

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  3. anonymous
    • one year ago
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    Graph 3

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  4. anonymous
    • one year ago
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    Graph 4

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  5. anonymous
    • one year ago
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    Graph 5

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  6. anonymous
    • one year ago
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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")

  7. anonymous
    • one year ago
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    do you know how to find the vertical asymptotes ?

  8. anonymous
    • one year ago
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    I am not sure how to do that. I was sadly not introduced throughly to the unit :(

  9. anonymous
    • one year ago
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    http://www.purplemath.com/modules/asymtote.htm

  10. anonymous
    • one year ago
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    @Hero @pooja195 @triciaal

  11. anonymous
    • one year ago
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    Yeah I am not totally understanding how to relate that to finding domain and range i'm a bit confused

  12. Loser66
    • one year ago
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    For the first one, \(f(x) = \dfrac{1}{x+1}\) take denominator =0, solve for x, what do you get?

  13. Loser66
    • one year ago
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    knock knock!!! x +1 =0, x =??

  14. anonymous
    • one year ago
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    ok! one moment

  15. anonymous
    • one year ago
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    -1 ?

  16. Loser66
    • one year ago
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    yes, domain relate to x, right? but you can't take x =-1 since it makes the function undefined, right? Hence D = \(\mathbb R/{-1}\)

  17. anonymous
    • one year ago
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    So that would make the domain for the first graph undefined then?

  18. Loser66
    • one year ago
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    How about the range? Look at the graph, y goes from -infinitive to +infinitive but at 0, Hence Range is \(\mathbb R/0\)

  19. Loser66
    • one year ago
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    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

  20. anonymous
    • one year ago
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    ahhhhhhhhhhhhh. That makes sense. I understand. I never understood the "all real numbers except.. ext."

  21. anonymous
    • one year ago
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    i'm sorry, I do not understand the notation- by "R/0" you mean that the range is all real numbers but 0?

  22. anonymous
    • one year ago
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    I only ask because I have to format it in sentence form

  23. Loser66
    • one year ago
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    yup

  24. Loser66
    • one year ago
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    it is not R/0. It is \(\mathbb R/\{0\}\). That the correct notation.

  25. anonymous
    • one year ago
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    Yes. My computer would not let me copy that. That is what I meant

  26. anonymous
    • one year ago
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    Would you mind helping me with the others?

  27. Loser66
    • one year ago
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    what is the second function? \(f(x) = \dfrac{1}{x-2}+1\)??

  28. anonymous
    • one year ago
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    x would equal 2 here. would this mean that the domain is all real numbers except for 2?

  29. Loser66
    • one year ago
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    yup

  30. anonymous
    • one year ago
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    and how would I find the range? i did not totally understand how you did that for the first graph

  31. Loser66
    • one year ago
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    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|

  32. Loser66
    • one year ago
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    for domain, you see that x goes from -infinitive to + infinitive except x =2|dw:1438655384625:dw|

  33. Loser66
    • one year ago
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    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 \(\mathbb R/\{1\}\)

  34. anonymous
    • one year ago
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    ok. I understand

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