Question
Compare the parent functions in the following answer choices. Which parent function is periodic and has an intercept at (0,1) ? (1 point) y=cos x y=tan x y=sin x y=10^x
Answers
GPT-4o mini
The periodic functions among the given options are \(y = \cos x\) and \(y = \sin x\).
Both of these functions have intercepts at (0,1):
- For \(y = \cos x\), when \(x = 0\), \(y = \cos(0) = 1\). So it has an intercept at (0,1).
- For \(y = \sin x\), when \(x = 0\), \(y = \sin(0) = 0\). So it does not have an intercept at (0,1).
The function \(y = \tan x\) is also periodic, but it does not have the intercept at (0,1); instead, it intercepts the y-axis at (0,0).
The function \(y = 10^x\) is not periodic.
Therefore, the correct answer to the question is **\(y = \cos x\)**, as it is the only periodic function with an intercept at (0, 1).
Both of these functions have intercepts at (0,1):
- For \(y = \cos x\), when \(x = 0\), \(y = \cos(0) = 1\). So it has an intercept at (0,1).
- For \(y = \sin x\), when \(x = 0\), \(y = \sin(0) = 0\). So it does not have an intercept at (0,1).
The function \(y = \tan x\) is also periodic, but it does not have the intercept at (0,1); instead, it intercepts the y-axis at (0,0).
The function \(y = 10^x\) is not periodic.
Therefore, the correct answer to the question is **\(y = \cos x\)**, as it is the only periodic function with an intercept at (0, 1).