To determine the amplitude of the function [tex]\( y = -2 \sin (3 \pi x) \)[/tex], we need to understand the general form of a sine function, which is given by:
[tex]\[ y = A \sin (Bx + C) \][/tex]
In this general form:
- [tex]\( A \)[/tex] represents the amplitude.
- [tex]\( B \)[/tex] affects the period of the function.
- [tex]\( C \)[/tex] represents the phase shift.
The amplitude of the function [tex]\( y = A \sin (Bx + C) \)[/tex] is given by the absolute value of [tex]\( A \)[/tex].
Given the specific function [tex]\( y = -2 \sin (3 \pi x) \)[/tex], we can identify the value of [tex]\( A \)[/tex]:
- Here, [tex]\( A = -2 \)[/tex].
The amplitude is the absolute value of [tex]\( A \)[/tex], which means:
[tex]\[ \text{Amplitude} = |A| \][/tex]
Substituting the given value of [tex]\( A \)[/tex]:
[tex]\[ \text{Amplitude} = |-2| = 2 \][/tex]
Thus, the amplitude of the function [tex]\( y = -2 \sin (3 \pi x) \)[/tex] is [tex]\( 2 \)[/tex].
