6 points possible answered: 0/6 question 1 for each function, determine the long run behavior. (x^2 +…

6 points possible answered: 0/6 question 1 for each function, determine the long run behavior. (x^2 + 1)/(x^2 + 2) has select an answer (x^3 + 1)/(x^2 + 2) has select an answer (x^2 + 1)/(x^3 + 2) has select an answer no horizontal asymptote a horizontal asymptote at y=0 a horizontal asymptote at y=1 > next

6 points possible answered: 0/6 question 1 for each function, determine the long run behavior. (x^2 + 1)/(x^2 + 2) has select an answer (x^3 + 1)/(x^2 + 2) has select an answer (x^2 + 1)/(x^3 + 2) has select an answer no horizontal asymptote a horizontal asymptote at y=0 a horizontal asymptote at y=1 > next

Answer

Explanation:

Step1: Recall horizontal - asymptote rules

For a rational function $y = \frac{f(x)}{g(x)}=\frac{a_nx^n+\cdots+a_0}{b_mx^m+\cdots + b_0}$, if $n = m$, the horizontal asymptote is $y=\frac{a_n}{b_m}$; if $n<m$, the horizontal asymptote is $y = 0$; if $n>m$, there is no horizontal asymptote.

Step2: Analyze $\frac{x^{2}+1}{x^{2}+2}$

Here $n = m=2$, $a_n = 1$, $b_m = 1$. So $y=\frac{1}{1}=1$. It has a horizontal asymptote at $y = 1$.

Step3: Analyze $\frac{x^{3}+1}{x^{2}+2}$

Here $n = 3$, $m = 2$, $n>m$. So it has no horizontal asymptote.

Step4: Analyze $\frac{x^{2}+1}{x^{3}+2}$

Here $n = 2$, $m = 3$, $n<m$. So it has a horizontal asymptote at $y = 0$.

Answer:

  1. a Horizontal asymptote at y=1
  2. No horizontal asymptote
  3. a Horizontal asymptote at y=0