Question #7256d

Aug 4, 2016

$f \left(x\right) \in \left[- 1 , 1\right]$

Explanation:

As you know, the range of the function

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

is limited to values that are greater than or equal to $- 1$ and smaller than or equal to $1$.

graph{sinx [-10, 10, -1.5, 1.5]}

This means that regardless of the value of $x$ you plug into the function, the output must always satisfy these two conditions

$f \left(x\right) \ge - 1 \text{ }$ and $\text{ } f \left(x\right) \le 1$

In interval notation, the range of the function is any real number that is part of the interval

$f \left(x\right) \in \left[- 1 , 1\right]$

Here the left bracket symbolizes $f \left(x\right) \ge - 1$ and the right bracket symbolizes $f \left(x\right) \le 1$.