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777dan777 [17]
3 years ago
5

2) translate into an equation

Mathematics
1 answer:
Butoxors [25]3 years ago
6 0
-4 - 7 divide 8n thats the answer
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How do you find the amplitude, period, and shift for f(x)=−4cos(3x−π)+1?
Orlov [11]

Answer:

(a) Amplitude = 4

(b) T = \frac{2\pi}{3} --- Period

(c)

C = \frac{\pi}{3} --- phase shift

D =1 --- vertical shift

Step-by-step explanation:

Given

f(x) = -4\cos(3x - \pi) + 1

Rewrite the function as:

f(x) = -4\cos(3(x - \frac{\pi}{3}) + 1

Solving (a): The amplitude

A cosine function is represented as:

f(x) = A\cos[B(x - C)] + D

Where:

|A| \to Amplitude

So, in this equation (by comparison):

|A| = |-4|

|A| = 4

<em>The amplitude is 4</em>

Solving (b): The period (T)

This is calculated as:

T = \frac{2\pi}{B}

By comparison:

B =3

So:

T = \frac{2\pi}{3}

Solving (c): The shift

The phase shift is C

The vertical shift is D

By comparison:

C = \frac{\pi}{3} --- phase shift

D =1 --- vertical shift

3 0
3 years ago
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