Help with figuring out the end behavior of a Rational

VorkDesegroorrta

VorkDesegroorrta

Answered question

2022-02-18

Help with figuring out the end behavior of a Rational Function.
What is the end behavior of:
f(x)=2x2+2x2+9
Any help would be good

Answer & Explanation

Jenson Mcculloch

Jenson Mcculloch

Beginner2022-02-19Added 9 answers

f(x)=2x2+2x2+9=2(x2+9)+22(9)x2+9=2(x2+9)16x2+9=216x2+9
As x is large, the term in blue will vanish, as the denominator have far bigger magnitude compared to the numerator. Hence the limit would be 2.
Of course, not every rational number will have their numerator and denominator to have the same degree.
Try to write
p(x)q(x)=t(x)+p1(x)q1(x)
where degree of p1(x) is smaller than degree of q1(x). As x is huge, p1(x)q1(x) becomes close to 0 and it will behave like t(x).
Gene Espinosa

Gene Espinosa

Beginner2022-02-20Added 7 answers

It helped a lot)

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