Question

What is the amplitude, period, and phase shift of f(x) = -4 sin(2x + π) - 5?

Answer 1

Answer:

Amplitude of the function is 4, period of the function is π and phase shift of the function is $-\frac{\pi}{2}$.

Step-by-step explanation:

The given function is

$f(x)=-4\sin(2x+\pi)-5$              .... (1)

The general form of a sine function is

$f(x)=A\sin(Bx+C)+D$            .... (2)

where, |A| is amplitude, $\frac{2\pi}{B}$ is period, $-\frac{C}{B}$ is phase shift and D is midline.

From (1) and (2) we get

$A=-4,B=2, C=\pi,D=-5$

$|A|=|-4|=4$

Amplitude of the function is 4.

$\frac{2\pi}{B}=\frac{2\pi}{2}=\pi$

Period of the function is π.

$-\frac{C}{B}=-\frac{\pi}{2}$

Therefore the phase shift of the function is $-\frac{\pi}{2}$.

Answer 2

F(x) = -4sin(2x + π) - 5

Amplitude
A = -π

Period
2π = 2π = π
 B      2

Phase Shift
-C = -π = ≈ 1.57
 B      2