15Twilight
Answered

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

Sagot :

Panoyin
f(x) = -4sin(2x + π) - 5

Amplitude
A = -π

Period
2π = 2π = π
 B      2

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

Answer:

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

Step-by-step explanation:

The given function is

[tex]f(x)=-4\sin(2x+\pi)-5[/tex]              .... (1)

The general form of a sine function is

[tex]f(x)=A\sin(Bx+C)+D[/tex]            .... (2)

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

From (1) and (2) we get

[tex]A=-4,B=2, C=\pi,D=-5[/tex]

[tex]|A|=|-4|=4[/tex]

Amplitude of the function is 4.

[tex]\frac{2\pi}{B}=\frac{2\pi}{2}=\pi[/tex]

Period of the function is π.

[tex]-\frac{C}{B}=-\frac{\pi}{2}[/tex]

Therefore the phase shift of the function is [tex]-\frac{\pi}{2}[/tex].

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