### Home > APCALC > Chapter 1 > Lesson 1.4.4 > Problem1-186

1-186.

Write an equation for the end-behavior function of f(x) = $\frac { x ^ { 3 } + 3 x ^ { 2 } - 4 x - 1 } { x ^ { 2 } - 1 }$. Then, write a complete set of approach statements for f. Homework Help ✎

This can be found using polynomial division.

$\frac{x^{3}+3x^{2}-4x-1}{x^{2}-1}=x+3+\frac{-3x+2}{x^{2}-1}$

Make sure to show your steps.

b(x) = x + 3

$\text{The term }\frac{-3x+2}{x^{2}-1}\text{ is insignificant for a large positive and negative }x.$

How does the graph behave as x approaches ∞, −∞, as well as the asymptotes 1 and −1 from both the positive and negative sides.