To find the amplitude of the function [tex]\( f(x) = 8 \sin \left(6 x + \frac{\pi}{4} \right) - 3 \)[/tex], we need to consider the general form of a sinusoidal function, which is given by:
[tex]\[ f(x) = A \sin(Bx + C) + D \][/tex]
In this general form:
- [tex]\( A \)[/tex] is the amplitude
- [tex]\( B \)[/tex] affects the period
- [tex]\( C \)[/tex] is the phase shift
- [tex]\( D \)[/tex] is the vertical shift
For the function [tex]\( f(x) = 8 \sin \left( 6x + \frac{\pi}{4} \right) - 3 \)[/tex], we identify the amplitude [tex]\( A \)[/tex] as the coefficient of the sine function. The coefficient of [tex]\(\sin\)[/tex] here is 8.
Thus, the amplitude of the function [tex]\( f(x) = 8 \sin \left(6 x + \frac{\pi}{4} \right) - 3 \)[/tex] is:
[tex]\[
\boxed{8}
\][/tex]
