Respuesta :
Answer:
The answer is A) amplitude: 3; period: pie/2; phase shift: x= pie/4; midline: y=2
For given sinusoidal function f(x) = -3 sin(4x - n) + 2,
amplitude: 3; period: π/2; phase shift: π/4; midline: y = 2
The correct answer is an option (A)
What is general form sinusoidal function?
"y = A sin(B(x - C)) + D,
The variables A , B, C, and D are called parameters."
What is amplitude of sinusoidal function?
"The amplitude of the sinusoidal functions y = A sin(B(x - C)) + D and is the absolute value of the parameter A ."
What is period of sinusoidal function?
"The period P of the sinusoidal functions y = A sin(B(x - C)) + D is [tex]P=\frac{2\pi}{B}[/tex] "
What is midline of sinusoidal function?
- "The midline of a sinusoidal function is the y -value that the function oscillates above and below."
- "The equation for the midline of a sinusoidal function is y = D"
What is phase shift of sinusoidal function?
- "The phase shift of sinusoidal function y = A sin(B(x - C)) + D is C."
- "It is positive is to the left."
For given question,
We have been given a sinusoidal function f(x) = -3 sin(4x - π) + 2
We can write given sinusoidal function as, f(x) = -3 sin(4(x - π/4)) + 2
Comparing given equation with sinusoidal function y = A sin(B(x - C)) + D,
we have A = -3, B = 4, C = π/4 , D = 2
Using the definition of amplitude,
an amplitude of given sinusoidal function is:
⇒ |A| = |-3|
⇒ |A| = 3
So, the amplitude of given sinusoidal function is 3.
Using the definition of period of sinusoidal function,
[tex]\Rightarrow P=\frac{2\pi}{B}\\\\\Rightarrow P=\frac{2\pi}{4} \\\\\Rightarrow P=\frac{\pi}{2}[/tex]
So, the period of given sinusoidal function f(x) = -3 sin(4x - n) + 2 is [tex]\frac{\pi}{2}[/tex]
Using the definition of phase shift of sinusoidal function,
Phase shift (C) = π/4
Using the definition of midline of sinusoidal function,
midline of given sinusoidal function is y = 2
Therefore, for given sinusoidal function f(x) = -3 sin(4x - n) + 2,
amplitude: 3; period: π/2; phase shift: π/4; midline: y = 2
The correct answer is an option (A)
Learn more about sinusoidal function here:
https://brainly.com/question/12060967
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