Define \(f\) as follows.
\[ f(k) = \begin{cases} \frac {3}{4} + 2 & \text { if } -8 \leq k < 0 \\ -\frac {3}{2} + 6 & \text { if } 4 \leq k \leq 8 \end{cases} \]

Graph of \(z = f(k)\).

Define \(g\) as follows.

\[ g(x) = -\frac {1}{4} - \frac {3}{2} \, \text { with domain } \, [-2, 6) \]

Graph of \(y = g(x)\).

To investigate the function \(g \circ f\) we need the range of \(f\) and the domain of \(g\).

The range of \(f\) is \(\left [ \answer {-8}, \answer {2} \right )\).

The domain of \(g\) is \(\left [ \answer {-2}, \answer {6} \right )\).

Their intersection is \(\left [ -2, 2 \right )\).

2025-05-17 16:18:13