### Home > APCALC > Chapter 4 > Lesson 4.4.3 > Problem4-166

4-166.

For each of the following functions, write an equation for the end-behavior function.

1. $y = \frac { 6 } { x } + 2 x ^ { 2 }$

$\text{Consider }\lim \limits_{x\rightarrow \infty }\frac{6}{x}+2x^{2}.$

$\text{What happens to the }\frac{6}{x}?$

2. $y = \frac { \operatorname { sin } ( x ) } { x }$

If a function has a horizontal asymptote, then that is the end behavior.

3. $y = \frac { x ^ { 2 } - 3 x - 10 } { x ^ { 2 } + 1 }$

If a function has a horizontal asymptote, then that is the end behavior. You can find a horizontal asymptote by evaluating

$\lim \limits_{x\rightarrow \infty }f(x).$