Question
Compare the parent functions in the following answer choices. Which parent function is periodic and has an intercept at (0,1)
?(1 point)
Responses
y=cosx
y equals cosine x
y=tanx
y equals tangent x
y=10x
y equals 10 superscipt x baseline
y=sinx
?(1 point)
Responses
y=cosx
y equals cosine x
y=tanx
y equals tangent x
y=10x
y equals 10 superscipt x baseline
y=sinx
Answers
GPT-4o mini
To find the periodic parent function with an intercept at (0, 1), we can analyze the given options:
1. **y = cos(x)**: The cosine function is periodic, with a period of \(2\pi\). It has an intercept at (0, 1) because \(\cos(0) = 1\).
2. **y = tan(x)**: The tangent function is periodic, but it has vertical asymptotes and does not have an intercept at (0, 1). Instead, \(\tan(0) = 0\).
3. **y = 10^x**: This is an exponential function, not periodic. It has an intercept at (0, 1) because \(10^0 = 1\), but it does not satisfy the periodicity requirement.
4. **y = sin(x)**: The sine function is periodic with a period of \(2\pi\), but it has an intercept at (0, 0) because \(\sin(0) = 0\).
Based on this analysis, the correct choice is:
**y = cos(x)**.
It is periodic and has an intercept at (0, 1).
1. **y = cos(x)**: The cosine function is periodic, with a period of \(2\pi\). It has an intercept at (0, 1) because \(\cos(0) = 1\).
2. **y = tan(x)**: The tangent function is periodic, but it has vertical asymptotes and does not have an intercept at (0, 1). Instead, \(\tan(0) = 0\).
3. **y = 10^x**: This is an exponential function, not periodic. It has an intercept at (0, 1) because \(10^0 = 1\), but it does not satisfy the periodicity requirement.
4. **y = sin(x)**: The sine function is periodic with a period of \(2\pi\), but it has an intercept at (0, 0) because \(\sin(0) = 0\).
Based on this analysis, the correct choice is:
**y = cos(x)**.
It is periodic and has an intercept at (0, 1).