CPM Homework Help : PC Problem 5-85

Use a graphing calculator to sketch the graph of $f\left(x\right) = x^{3} − 3x − 2$ . Use the graph to find all the vertical asymptotes of $\frac { 1 } { f ( x ) }$ .

Hint:

Where does $f\left(x\right) = 0$ ?

Curve coming from lower left, turning down at (negative 1, comma 0), turning up at (1, comma negative 4), passing through (2, comma 0), continuing up & right.

Graph:

$\frac{1}{f(x)}$

Rational function with 3 pieces, left piece coming from below x axis, decreasing to negative infinity, left of x = negative 1, center piece, coming from negative infinity right of x = negative 1, turning at approximately (1 half, comma 1 fourth), going to negative infinity left of x = 2, right piece, coming from infinity right of x = 2, continuing to right above x axis.