What are the amplitude, period, phase shift, and midline of f(x) = −3 sin(4x − π) + 2? (6 points)
amplitude: 3; period: pi over 2 ; phase shift: x = pi over 4 ; midline: y = 2
amplitude: −3; period: pi over 2 ; phase shift: x = pi over 2 ; midline: y = 2
amplitude: 2; period: pi over 4 ; phase shift: x = pi over 4 ; midline: y = −3
amplitude: 2; period: pi over 4 ; phase shift: x = pi over 2 ; midline: y = −3

Amplitude: 3

period: π/2

Phase shift: π/4

Midline : y=2

Step-by-step explanation:

We are asked to find the amplitude, period, phase shift and midline of the given function f(x) as:

f(x)= -3 sin (4x-π)+2

f(x)= -3 sin (-(π-4x))+2

f(x)= -3 -( sin (π-4x))+2 ( since sin(-θ)=-sin (θ) )

f(x)=3 sin 4x+2 ( since sin (π-θ)=sin (θ) )

       Hence, the amplitude is 3 units.

       Hence, period of 4x is:

          2π/4=π/2.

         Hence, the phase shift is: π/4

        Hence, here we have midline y=2.

find the magnitude of the trig term  

csc

(

x

)

−

1

by taking the absolute value of the coefficient.

1

find the lower bound of the range.

tap for more

y

=

−

2

find the upper bound of the range.

tap for more

y

=

0

the range is  

y

≤

−

2

or  

y

≥

0

.

(

−

∞

,

−

2

]

∪

[

0

,

∞

)

{

y

|

y

≤

−

2

,

y

≥

0

}

step-by-step explanation:

80 the answer is 80

step-by-step explanation: