\[ f(k) = \begin{cases} \frac {3}{4} + 2 & \text { if } -8 \leq k < 0 \\ -\frac {3}{2} + 6 & \text { if } 4 \leq k \leq 8 \end{cases} \]
Graph of \(z = f(k)\).
![[Picture]](example_3-b0569166f98a68ea3d7548a9931c431b.svg)
Define \(g\) as follows.
\[ g(x) = -\frac {1}{4} - \frac {3}{2} \, \text { with domain } \, [-2, 6) \]
Graph of \(y = g(x)\).
![[Picture]](example_3-ce2fb68f93454450a19f64c14d5b90d2.svg)
To investigate the function \(f \circ g\) we need the range of \(g\) and the domain of \(f\).
The range of \(g\) is \(\left [ \answer {-2}, \answer {0} \right )\).
The domain of \(f\) is \(\left [ \answer {-8}, \answer {0} \right ) \cup \left [ 4, 8 \right )\).
Their intersection is \(\left [ -2, 0 \right )\).