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