Chapter 14.3, Problem 88AYU

To determine

To find: The graph of $R\left(x\right)$.

Answer to Problem 88AYU

Explanation of Solution

Given:

$R\left(x\right) = \frac{x^3 - 3x^2 + 4x - 12}{x^4 - 3x^3 + x - 3}$

Calculation:

$R\left(x\right) = \frac{x^3 - 3x^2 + 4x - 12}{x^4 - 3x^3 + x - 3}$

$R\left(x\right) = \frac{\left(x^2 + 4\right)\left(x - 3\right)}{\left(x^3 + 1\right)\left(x - 3\right)}$

$R\left(x\right) = \frac{\left(x^2 + 4\right)}{\left(x^3 + 1\right)}$

Graph of $R$ is as follows: