Question

Compare the parent functions in the following answer choices. Which parent function is periodic and has an intercept at (0,1)?
A. y=tanx
B. y=sinx
C. y=10
x

D. y=cosx

Answer 1

To determine which parent function is periodic and has an intercept at (0,1), let's analyze each of the answer choices:

A. \( y = \tan x \)
- The tangent function is periodic with a period of \( \pi \), but its value at \( x = 0 \) is \( 0 \), so it does not have an intercept at (0,1).

B. \( y = \sin x \)
- The sine function is periodic with a period of \( 2\pi \), and at \( x = 0 \), \( \sin(0) = 0 \), so it does not have an intercept at (0,1).

C. \( y = 10 \)
- This is a constant function that is not periodic. It does not have any intercepts at (0,1) because it is always at \( y = 10 \).

D. \( y = \cos x \)
- The cosine function is also periodic with a period of \( 2\pi \), and at \( x = 0 \), \( \cos(0) = 1 \). Therefore, it has an intercept at (0,1).

Based on this analysis, the periodic parent function that has an intercept at (0,1) is:

**D. \( y = \cos x \)**