Answer:
The required function is f(x)=4sinx-1.
Step-by-step explanation:
The standard sine function is defined as
[tex]f(x)=a\sin(b(x+c))+d[/tex] ....(1)
Where a is amplitude, period is [tex]\frac{2\pi }{b}[/tex], c is phase shift and d is midline.
It is given that the maximum value is 3 and the minimum value is -5. Amplitude is half of difference between minimum and maximum.
[tex]a=\frac{3-(-5)}{2}=4[/tex]
The value of a is 4.
The period is 2π.
[tex]\frac{2\pi}{b}=2\pi[/tex]
[tex]b=1[/tex]
Midline is average of maximum and minimum.
[tex]d=\frac{3-5}{2}=-1[/tex]
Substitute a=4, b=1, c=0 and d=1 in equation (1).
[tex]f(x)=4\sin(x)-1[/tex]
Therefore the required function is f(x)=4sinx-1.
