(A) Given the function $f(x) = x$ defined on the interval $[-1, 1]$.To determine the nature of the function,we find its derivative with respect to $x$

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(A) Given the function $f(x) = x$ defined on the interval $[-1, 1]$.To determine the nature of the function,we find its derivative with respect to $x$:$f'(x) = \frac{d}{dx}(x) = 1$.Since $f'(x) = 1 > 0$ for all $x \in [-1, 1]$,the function $f(x)$ is strictly increasing on the given interval.Therefore,the correct option is $A$.