Compare the parent functions in the following answer choices. Which parent function has positive and negative intervals and crosses through the origin?(1 point)

Question

Responses

y=sinx
y equals sine x

y=x2
y equals x squared

y=logx
y equals logarithm x

y=cosx

Answer 1

The parent function that has positive and negative intervals and crosses through the origin is \( y = \sin x \).

Here's a brief comparison of the functions:

1. \( y = \sin x \): This function oscillates between -1 and 1, has positive intervals (between \(0\) and \(\pi\)) and negative intervals (between \(\pi\) and \(2\pi\)), and it crosses through the origin at point \((0, 0)\).

2. \( y = x^2 \): This is a parabolic function that opens upwards, meaning it is always positive (except at the origin, where it is zero). It does not have negative intervals.

3. \( y = \log x \): This function is only defined for \(x > 0\), so it doesn't cross through the origin and does not exhibit negative intervals.

4. \( y = \cos x \): This function oscillates between -1 and 1 and does cross through the y-axis at \( (0, 1) \), but it does not cross through the origin.

Therefore, the answer is \( y = \sin x \).