Question

which of the following is the correct domain, range, and y-intercept for $y = \cos x$?
domain: select
range: select
$\\{ x | x \in \mathbb{r} \\}$
$\\{ x | -1 \leq x \leq 1 \\}$
y-intercept: $(0, 1)$

Explanation:

Step1: Identify domain of $y=\cos x$

The cosine function is defined for all real numbers, so domain is $\{x \mid x \in \mathbb{R}\}$.

Step2: Identify range of $y=\cos x$

The cosine function outputs values between -1 and 1 inclusive, so range is $\{x \mid -1 \leq x \leq 1\}$.

Step3: Identify y-intercept of $y=\cos x$

Substitute $x=0$: $y=\cos(0)=1$, so y-intercept is $(0,1)$.

Answer:

Domain: $\boldsymbol{\{x \mid x \in \mathbb{R}\}}$
Range: $\boldsymbol{\{x \mid -1 \leq x \leq 1\}}$
y-intercept: $\boldsymbol{(0, 1)}$