\[ P(t) = \begin{cases} ln(t+8) & \text { on } (-8, -3] \\ -4 & \text { if } t = -2 \\ | t - 3 | - 4 & \text { on } (0, 8] \end{cases} \]
![[Picture]](domain_2-5f31d86da25a9766a7b0f3d419a68c7c.svg)
Domain of \(P\)
What is the domain of \(P\)?
\[ \left ( \answer {-8} , \answer {-3} \right ] \cup \{ -2 \} \cup \left ( \answer {0} , \answer {8} \right ] \]
Shifted Domain
Define \(M(y) = P(y - 2)\)
What is the connection between the domain variables?
\[ t = \answer {y-2} \, \text { and } \, y = \answer {t+2} \]
What is the domain of \(M\)?
\[ \left ( \answer {-6} , \answer {-1} \right ] \cup \{ 0 \} \cup \left ( \answer {2} , \answer {10} \right ] \]
Shifted Domain
Define \(x(f) = V(f + 3)\)
What is the connection between the domain variables?
\[ t = \answer {f+3} \, \text { and } \, f = \answer {t-3} \]
What is the domain of \(G\)?
\[ \left ( \answer {-11} , \answer {-6} \right ] \cup \{ -5 \} \cup \left ( \answer {-3} , \answer {5} \right ] \]