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unicwaan

  • one year ago

I need to find the domain and range, x and y intercepts, horizontal and vertical asymptotes. Can someone help me through it please?

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  1. anonymous
    • one year ago
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    Hi what is your function?

  2. unicwaan
    • one year ago
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    There should be a picture attached but it's: X^2 + x - 2 divided by x^2 - 3x - 4

  3. anonymous
    • one year ago
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    first thing, you should factor the num and denom of your function\[f(x)=\frac{x^2+x-2}{x^2-3x-4}\]have you tried to do so?

  4. unicwaan
    • one year ago
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    I did, the numerator factors into (x-1)(x+2) and the deniminator factors into (x-4)(x+1)

  5. anonymous
    • one year ago
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    very good, so what will be the domain considering the denom?

  6. unicwaan
    • one year ago
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    The domain would be all reals except x=4 and x=-1?

  7. anonymous
    • one year ago
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    quite right

  8. anonymous
    • one year ago
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    let's work on range of the function

  9. unicwaan
    • one year ago
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    alright

  10. unicwaan
    • one year ago
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    Is the range all reals?

  11. anonymous
    • one year ago
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    thats right, do you have a reasoning for that?

  12. unicwaan
    • one year ago
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    Well by the graph it extends infinitely up and down

  13. unicwaan
    • one year ago
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    and because quadratic functions' range will always be all reals

  14. anonymous
    • one year ago
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    that's right, but what if we don't know about the graph

  15. anonymous
    • one year ago
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    note that quadratics don't cover all reals|dw:1434182772266:dw|

  16. unicwaan
    • one year ago
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    Oh okay, then I do not a reasoning

  17. unicwaan
    • one year ago
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    do not have a reasoning*

  18. anonymous
    • one year ago
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    function is continuous on the interval (-1,4) and\[\lim_{x \to -1^{+}} f(x)=\infty \]\[\lim_{x \to 4^{-}} f(x)=-\infty \]therefore range is all of real numbers

  19. anonymous
    • one year ago
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    does that make sense?

  20. unicwaan
    • one year ago
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    So when you plugged in the ordered pair, the output was infinite basically?

  21. anonymous
    • one year ago
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    thats right

  22. unicwaan
    • one year ago
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    okay that makes sense

  23. anonymous
    • one year ago
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    for example\[\lim_{x \to -1^{+}} f(x)=\frac{1 \times -2}{-5 \times 0^{+}}=\infty\]

  24. anonymous
    • one year ago
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    ok what are x and y intercepts?

  25. unicwaan
    • one year ago
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    Alright so the y intercept = 1/2 because you plug in 0 for x to find y. The x intercept = -2,1 because they are the zeros of the numerator

  26. anonymous
    • one year ago
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    very right, thanks

  27. anonymous
    • one year ago
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    and what about asymptotes

  28. unicwaan
    • one year ago
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    The horizontal asymptotes is 1 because the degree of each function are the same and therefore, must divide the leading coeeficients. The vertical asymptotes are y= -1,4 because they are the zeros of the denominator.

  29. anonymous
    • one year ago
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    right, you can put your words in mathematical phrases

  30. anonymous
    • one year ago
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    now you can graph your function

  31. unicwaan
    • one year ago
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    Okay so for the asympotes I put dotted lines to represent them, and then I plugged in points according to get this graph|dw:1434183896630:dw| Poor drawing but the basic jist of it :/

  32. anonymous
    • one year ago
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    we're done

  33. unicwaan
    • one year ago
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    Great! Thank you so much this really helped! :D

  34. anonymous
    • one year ago
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    no problem

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