In general, the range of the sine function is
[tex]sin(y)\in\lbrack-1,1\rbrack[/tex]Therefore, in the case of f(x),
[tex]sin(\frac{7x}{3}+\frac{1}{6})\in\lbrack-1,1\rbrack,x\in\Re[/tex]Thus, as for the minimum and maximum values of f(x),
[tex]\begin{gathered} \Rightarrow f(x)=-19*-1-3=19-3=16\rightarrow\text{ maximum} \\ and \\ f(x)=-19*1-3=-19-3=-22\rightarrow\text{ minimum} \end{gathered}[/tex]This, the answer is 'from a low temperature of -22°F to a high of 16°F'