# Over what domain is f(x)=sin(x) continuous ?

Dec 9, 2016

$f \left(x\right)$ is continuous $\forall x \in \mathbb{R}$

#### Explanation:

$f \left(x\right) = \sin x$

$f \left(x\right)$ is continuous $\forall x \in \mathbb{R}$

The domain of $f \left(x\right)$ is $\left(- \infty , + \infty\right)$

The range of $f \left(x\right)$ is $\left[- 1 , + 1\right]$

A portion of the graph of $f \left(x\right)$ about the origin is shown below:

graph{sinx [-6.244, 6.244, -3.12, 3.123]}