haleyelizabeth2017
  • haleyelizabeth2017
Determine the equation of the horizontal asymptotes, if any, of the function. f(x)=4/x^2+1)
Mathematics
  • Stacey Warren - Expert brainly.com
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katieb
  • katieb
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jim_thompson5910
  • jim_thompson5910
it's this right? \[\Large f(x) = \frac{4}{x^2+1}\]
haleyelizabeth2017
  • haleyelizabeth2017
Yes :)
jim_thompson5910
  • jim_thompson5910
|dw:1444170111505:dw|

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jim_thompson5910
  • jim_thompson5910
rewrite 4 as 4*1 |dw:1444170139532:dw|
jim_thompson5910
  • jim_thompson5910
the 1 up top can be written as \(\Large x^0\) |dw:1444170171324:dw|
jim_thompson5910
  • jim_thompson5910
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|
jim_thompson5910
  • jim_thompson5910
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
jim_thompson5910
  • jim_thompson5910
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
haleyelizabeth2017
  • haleyelizabeth2017
Good rule to know.

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