Answer:
(a) Amplitude = 4
(b) [tex]T = \frac{2\pi}{3}[/tex] --- Period
(c)
[tex]C = \frac{\pi}{3}[/tex] --- phase shift
[tex]D =1[/tex] --- vertical shift
Step-by-step explanation:
Given
[tex]f(x) = -4\cos(3x - \pi) + 1[/tex]
Rewrite the function as:
[tex]f(x) = -4\cos(3(x - \frac{\pi}{3}) + 1[/tex]
Solving (a): The amplitude
A cosine function is represented as:
[tex]f(x) = A\cos[B(x - C)] + D[/tex]
Where:
[tex]|A| \to Amplitude[/tex]
So, in this equation (by comparison):
[tex]|A| = |-4|[/tex]
[tex]|A| = 4[/tex]
The amplitude is 4
Solving (b): The period (T)
This is calculated as:
[tex]T = \frac{2\pi}{B}[/tex]
By comparison:
[tex]B =3[/tex]
So:
[tex]T = \frac{2\pi}{3}[/tex]
Solving (c): The shift
The phase shift is C
The vertical shift is D
By comparison:
[tex]C = \frac{\pi}{3}[/tex] --- phase shift
[tex]D =1[/tex] --- vertical shift
