Question

find the oblique asymptote and sketch the graph of the rational function. f(x) = (3x^2 - x)/(x - 3) find the oblique asymptote. y = (simplify your answer.)

Explanation:

Step1: Perform polynomial long - division

Divide $3x^{2}-x$ by $x - 3$. We know that $3x^{2}-x=3x(x - 3)+9x - x=3x(x - 3)+8x=3x(x - 3)+8(x - 3)+24$. So, $\frac{3x^{2}-x}{x - 3}=3x + 8+\frac{24}{x - 3}$.

Step2: Determine the oblique asymptote

As $x\to\pm\infty$, the term $\frac{24}{x - 3}\to0$. The oblique asymptote is given by the non - remainder part of the long - division result.

Answer:

$y = 3x+8$