Question

Micah

Answer 1

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.