Compare the parent functions in the following answer choices. Which parent function is periodic and has an intercept at (0,1)

Question

?(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

Answer 1

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)).