Given:
The function f represents the diver's distance from sea level over time, in seconds.
[tex]f(x)=\begin{cases}3x+1 & \text{ if } -9<x\leq -2 \\ -5 & \text{ if } -2<x\leq 1 \\ x-6 & \text{ if } 1<x<7 \end{cases}[/tex]
To find:
The correct statement for the domain.
Solution:
Domain is the set of input values for which the function is defined.
Here, x values are the input values and they represent time intervals on which the function is defined
Here, the possible intervals for x are [tex]-9<x\leq -2,-2<x\leq 1,1<x<7[/tex].
[tex]Domain=(-9,-2]\cup (-2,1]\cup (1,7)[/tex]
[tex]Domain=(-9,7)[/tex]
Therefore, the domain is the time interval (−9, 7). Hence the correct option is A.
