Question

check pictureOn the graph below, move the two points to graph the slant asymptote for the function f(x)=−x2−x+3−x−2.

Answer 1

Answer:

slant asymptote is f(x) = x - 1

see graph below

Explanation:

Given:

$f(x)\text{ = }\frac{-x^2\text{ - x + 3}}{-x-2}$

To find:

The slant asymptote and graph it

$\begin{gathered} Using\text{ long division:} \\ Quotient\text{ = x - 1} \\ remainder\text{ = 1} \\ \frac{-x^2\text{ - x + 3}}{-x-2}\text{ = \lparen x - 1\rparen + }\frac{1}{-x-2} \\ taking\text{ the limit, as x tends to }\infty,\text{ }\frac{1}{-x-2}\text{ tends to zero} \\ \\ we\text{ would be left with = x - 1} \\ The\text{ slant asymptote, f\lparen x\rparen = x - 1} \end{gathered}$

Graphing the equation on the same coordinate as the function: