### Home > PC > Chapter 8 > Lesson 8.2.1 > Problem8-72

8-72.

Given $f(x) = \frac { x ^ { 3 } - 7 x - 6 } { x + 1 }$.

1. What is the value of $f \left(−1\right)$?

What happens when the denominator is $0$?

2. Find $\lim\limits _ { x \rightarrow - 1 } f ( x )$. (Hint: polynomial division)

Substitute $x = −1$ into the quotient.

$\begin{array}{l} \qquad \quad x ^ { 2 } - x - 6 \\ x +1 \enclose{longdiv}{\; x ^ { 3 } + 0 x ^ { 2 } - 7 x - 6}\\ \qquad \underline{ - ( x ^ { 3 } + x ^ { 2 } )} \\ \qquad \qquad \quad \; \;- x ^ { 2 } - 7 x \\ \qquad \qquad \; \, \underline{- ( - x ^ { 2 } - 1 x )} \\ \qquad \qquad \qquad \qquad \; - 6 x - 6 \\ \qquad \qquad \qquad \quad \underline{-(-6x-)6}\\ \qquad \qquad \qquad \qquad \qquad 0 \end{array}$

3. Use what you found from part (b) to sketch $f\left(x\right)$ without using a calculator.

You know it is a parabola with a hole at $x = −1$. Find the $x$-intercepts by factoring.