\[ V(h) = \begin{cases} -3(h + 5) & \text { if } [-8, -4) \\ (h+2)(h-2) & \text { if } [-2, 2) \\ -5(h-5)(h-7) & \text { if } [5, 7] \end{cases} \]
![[Picture]](domain_1-fc59ca5fe6e5e119b308e25ba9540573.svg)
Domain of \(V\)
What is the domain of \(V\)?
\[ \left [ \answer {-8} , \answer {-4} \right ) \cup \left [ \answer {-2} , \answer {2} \right ) \cup \left [ \answer {5} , \answer {7} \right ] \]
Shifted Domain
Define \(f(x) = V(x - 3)\)
What is the connection between the domain variables?
\[ h = \answer {x-3} \, \text { and } \, x = \answer {h+3} \]
What is the domain of \(f\)?
\[ \left [ \answer {-5} , \answer {-1} \right ) \cup \left [ \answer {1} , \answer {5} \right ) \cup \left [ \answer {8} , \answer {10} \right ] \]
Shifted Domain
Define \(G(t) = V(t + 4)\)
What is the connection between the domain variables?
\[ h = \answer {t+4} \, \text { and } \, t = \answer {h-4} \]
What is the domain of \(G\)?
\[ \left [ \answer {-12} , \answer {-8} \right ) \cup \left [ \answer {-6} , \answer {-2} \right ) \cup \left [ \answer {1} , \answer {3} \right ] \]