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trig graph with points at 0, 2 and pi over 2, 5 and pi, 2 and 3 pi over 2, negative 1 and 2 pi, 2


What are the amplitude and midline?


Amplitude: 2; midline: y = 3

Amplitude: 1; midline: y = 3

Amplitude: 2; midline: y = 1

Amplitude: 3; midline: y = 2

Verified Answer :

Correct answer is D.

\(y=A\sin{x}+B\)
A - amplitude
y = B - midline

\(y=3\sin{x}+2\)
Amplitude: 3; midline: y = 2

Answer:

The correct option is 4. Amplitude: 3; midline: y = 2

Step-by-step explanation:

The graph passing through the points (0,2), \((\frac{\pi}{2},5),(\pi,2),(\frac{3\pi}{2},-1),(2\pi,2)\).

If a is maximum value and b is minimum value, then

\(Amplitude=\frac{a-b}{2}\)

\(Midline=\frac{a+b}{2}\)

The minimum value of the function is -1.

The maximum value of the function is 5.

\(Amplitude=\frac{5-(-1)}{2}=\frac{6}{2}=3\)

The amplitude of the graph is 3.

\(Midline=\frac{5+(-1)}{2}=\frac{4}{2}=2\)

The midline of the graph is y=2.

The general sine function is

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

Where, A is amplitude, 2π/B is period, C is phase shift and D is midline.

The required function is

\(f(x)=3\sin x+2\)

Therefore correct option is 4.

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