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 = 10^x
○ y = sin x
○ y = cos x
○ y = tan x

Explanation:

Step1: Check periodicity

A periodic function repeats its values at regular intervals.

• For \(y = 10^{x}\), it is an exponential function and is not periodic.
• For \(y=\sin x\), the period is \(2\pi\). For \(y = \cos x\), the period is \(2\pi\). For \(y=\tan x\), the period is \(\pi\).

Step2: Check the \(y -\)intercept

The \(y -\)intercept of a function \(y = f(x)\) is found by setting \(x = 0\).

• If \(x = 0\), for \(y = 10^{x}\), \(y=10^{0}=1\), but it is not periodic.
• If \(x = 0\), for \(y=\sin x\), \(y=\sin(0) = 0\).
• If \(x = 0\), for \(y=\cos x\), \(y=\cos(0)=1\).
• If \(x = 0\), for \(y=\tan x\), \(y=\tan(0) = 0\).

Answer:

\(y=\cos x\)