• Problem
• Detailed Solution
• Summary Solution

Let f be given by:

$f:x \to y = \frac{{ - {x^2} + 5x + 8}}{{2{x^2} - 8}}$

a) ${D_f} = \mathbb{R}\backslash \left\{ ? \right\}$

b) Determine the roots.

c) Determine the asymptotes.

d) Sketch the graph.

From our studies of rational functions (block I, learning sequence 2), we know the following

### a) Domain

The domain consists of all real numbers for which the denominator is different from 0. Thus, we have to determine the roots of

See here .