Duplicate Question
The question on this page has been marked as a duplicate question.
Original Question
Compare the parent functions in the following answer choices. Which parent function is periodic and has an intercept at (0,1) ?...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=10x
y equals 10 superscipt x baseline
y=tanx
y equals tangent x
y=sinx
y equals sine x
y=cosx
?(1 point)
Responses
y=10x
y equals 10 superscipt x baseline
y=tanx
y equals tangent x
y=sinx
y equals sine x
y=cosx
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To determine which parent function is periodic and has an intercept at (0, 1), let's analyze the given options:
1. **y = 10^x (Exponential Function)**: This function is not periodic. It passes through (0, 1) because \(10^0 = 1\), but it does not satisfy the periodicity condition.
2. **y = tan(x) (Tangent Function)**: This function is periodic, with a period of \(\pi\). However, it does not have an intercept at (0, 1). The value at x = 0 is \(tan(0) = 0\).
3. **y = sin(x) (Sine Function)**: This function is periodic with a period of \(2\pi\). At x = 0, \(sin(0) = 0\), so it does not have an intercept at (0, 1).
4. **y = cos(x) (Cosine Function)**: This function is also periodic with a period of \(2\pi\). At x = 0, \(cos(0) = 1\), which means it does have an intercept at (0, 1).
From these analyses, the correct answer is:
**y = cos(x)** (it is periodic and has an intercept at (0, 1)).
1. **y = 10^x (Exponential Function)**: This function is not periodic. It passes through (0, 1) because \(10^0 = 1\), but it does not satisfy the periodicity condition.
2. **y = tan(x) (Tangent Function)**: This function is periodic, with a period of \(\pi\). However, it does not have an intercept at (0, 1). The value at x = 0 is \(tan(0) = 0\).
3. **y = sin(x) (Sine Function)**: This function is periodic with a period of \(2\pi\). At x = 0, \(sin(0) = 0\), so it does not have an intercept at (0, 1).
4. **y = cos(x) (Cosine Function)**: This function is also periodic with a period of \(2\pi\). At x = 0, \(cos(0) = 1\), which means it does have an intercept at (0, 1).
From these analyses, the correct answer is:
**y = cos(x)** (it is periodic and has an intercept at (0, 1)).
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.