Question
a graph starts at -1pi, then has a repeated pattern of going up by 1, then down to -1.
This is the graph of the function (1.). It has a period of (2.) and the amplitude is equal to (3.)
1.
A. Y = cos x
B. Y = sin x
2.
A. 0
B. Pi
C. 1
D. 2pi
3.
A. 0
B. Pi
C. 1
D. 2pi
This is the graph of the function (1.). It has a period of (2.) and the amplitude is equal to (3.)
1.
A. Y = cos x
B. Y = sin x
2.
A. 0
B. Pi
C. 1
D. 2pi
3.
A. 0
B. Pi
C. 1
D. 2pi
Answers
GPT-4o mini
Based on your description of the graph, we can analyze it step by step.
1. **Function**: The graph starts at \(-\pi\) and then has a repeated pattern of going up by 1 and then down to \(-1\). This resembles a sine function that repeats with a vertical shift. Given that it likely resembles the behavior of sine or cosine, since it starts at a minimum value and goes up, the more suitable choice is:
- **A. Y = sin x** (since Y = sin x starts at 0 and can be adjusted to fit these characteristics with a phase shift).
2. **Period**: The period is the length of one complete cycle of the repeating pattern. Since it's going up by 1 and then returning down which forms a sinusoidal wave, we generally expect for basic sine and cosine functions that:
- The period of the sine and cosine functions is \(2\pi\). Thus, the answer is:
- **D. 2pi**.
3. **Amplitude**: The amplitude is half the distance between the maximum and minimum values of the function. If the function goes from \(-1\) to \(0\) and upwards to \(1\), the highest point being \(0\) and the lowest point being \(-1\) indicates an amplitude of:
- Amplitude \(= \frac{1 - (-1)}{2} = 1\). Hence, the answer is:
- **C. 1**.
So the final answers are:
1. A. Y = sin x
2. D. 2pi
3. C. 1
1. **Function**: The graph starts at \(-\pi\) and then has a repeated pattern of going up by 1 and then down to \(-1\). This resembles a sine function that repeats with a vertical shift. Given that it likely resembles the behavior of sine or cosine, since it starts at a minimum value and goes up, the more suitable choice is:
- **A. Y = sin x** (since Y = sin x starts at 0 and can be adjusted to fit these characteristics with a phase shift).
2. **Period**: The period is the length of one complete cycle of the repeating pattern. Since it's going up by 1 and then returning down which forms a sinusoidal wave, we generally expect for basic sine and cosine functions that:
- The period of the sine and cosine functions is \(2\pi\). Thus, the answer is:
- **D. 2pi**.
3. **Amplitude**: The amplitude is half the distance between the maximum and minimum values of the function. If the function goes from \(-1\) to \(0\) and upwards to \(1\), the highest point being \(0\) and the lowest point being \(-1\) indicates an amplitude of:
- Amplitude \(= \frac{1 - (-1)}{2} = 1\). Hence, the answer is:
- **C. 1**.
So the final answers are:
1. A. Y = sin x
2. D. 2pi
3. C. 1