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haleyelizabeth2017

  • one year ago

Determine the equation of the horizontal asymptotes, if any, of the function. f(x)=4/x^2+1)

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  1. jim_thompson5910
    • one year ago
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    it's this right? \[\Large f(x) = \frac{4}{x^2+1}\]

  2. haleyelizabeth2017
    • one year ago
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    Yes :)

  3. jim_thompson5910
    • one year ago
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    |dw:1444170111505:dw|

  4. jim_thompson5910
    • one year ago
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    rewrite 4 as 4*1 |dw:1444170139532:dw|

  5. jim_thompson5910
    • one year ago
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    the 1 up top can be written as \(\Large x^0\) |dw:1444170171324:dw|

  6. jim_thompson5910
    • one year ago
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    the largest exponent for the numerator is 0 so the degree of the numerator is 0 the largest exponent for the denominator is 2 so the degree of the denominator is 2 |dw:1444170219440:dw|

  7. jim_thompson5910
    • one year ago
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    Rule: If the degree of the numerator is smaller than the degree of the denominator, then the horizontal asymptote is always the line `y = 0`. Basically the x axis

  8. jim_thompson5910
    • one year ago
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    the denominator grows far faster than the numerator so as x gets larger, f(x) approaches 0 |dw:1444170311640:dw| it never actually gets to 0 though

  9. haleyelizabeth2017
    • one year ago
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    Good rule to know.

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