To determine the domain and range of the function [tex]\( p(t) = 5 \sin (880 \pi t) \)[/tex]:
1. Domain:
- The domain of the function is related to the time [tex]\( t \)[/tex] after the tuning fork is struck. Since time cannot be negative, [tex]\( t \)[/tex] must be non-negative.
- Therefore, the domain of the function is [tex]\( t \geq 0 \)[/tex].
2. Range:
- The function [tex]\( \sin \)[/tex] oscillates between -1 and 1.
- When the amplitude of the sine wave is multiplied by 5, the pressure change [tex]\( p(t) \)[/tex] will oscillate between [tex]\( 5 \times (-1) \)[/tex] and [tex]\( 5 \times 1 \)[/tex], which are -5 and 5 Pascals, respectively.
- Therefore, the range of the function is [tex]\( -5 \leq p(t) \leq 5 \)[/tex].
So, the final answer is:
The domain of the function is [tex]\( t \geq \)[/tex] 0.
The range of the function is -5 [tex]\( \leq p(t) \leq \)[/tex] 5.
