Question

Question
Which function has the largest amplitude?
(1 point)
Responses

f left parenthesis x right parenthesis equals negative 3 sine left parenthesis x minus Start Fraction pi over 4 End Fraction right parenthesis plus 1
Image with alt text: f left parenthesis x right parenthesis equals negative 3 sine left parenthesis x minus Start Fraction pi over 4 End Fraction right parenthesis plus 1

f left parenthesis x right parenthesis equals 2 cosine x plus 3
Image with alt text: f left parenthesis x right parenthesis equals 2 cosine x plus 3

f left parenthesis x right parenthesis equals sine left parenthesis 5 x plus Start Fraction 2 pi over 3 End Fraction right parenthesis minus 4
Image with alt text: f left parenthesis x right parenthesis equals sine left parenthesis 5 x plus Start Fraction 2 pi over 3 End Fraction right parenthesis minus 4

f left parenthesis x right parenthesis equals negative 2 cosine left parenthesis 4 x plus 3 pi right parenthesis minus 6
Image with alt text: f left parenthesis x right parenthesis equals negative 2 cosine left parenthesis 4 x plus 3 pi right parenthesis minus 6
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Answer 1

To determine which function has the largest amplitude, we can analyze the amplitude of each function:

1. **\( f(x) = -3 \sin\left(x - \frac{\pi}{4}\right) + 1 \)**
Amplitude = 3 (the coefficient of the sine function)

2. **\( f(x) = 2 \cos(x) + 3 \)**
Amplitude = 2 (the coefficient of the cosine function)

3. **\( f(x) = \sin\left(5x + \frac{2\pi}{3}\right) - 4 \)**
Amplitude = 1 (the coefficient of the sine function)

4. **\( f(x) = -2 \cos\left(4x + 3\pi\right) - 6 \)**
Amplitude = 2 (the coefficient of the cosine function)

Now, we compare the amplitudes:
- Function 1: 3
- Function 2: 2
- Function 3: 1
- Function 4: 2

The function with the largest amplitude is **\( f(x) = -3 \sin\left(x - \frac{\pi}{4}\right) + 1 \)**, which has an amplitude of 3.