Find the interval of continuity for function. Also, identify the endpoints for which the function is left-continuous or right-continuous.
$g\left(x\right)=\sqrt{289-x^2}$

$[-289,289]$,

Left-continuous at $-289$, right-continuous at $289$

$\(\left\[\lbrack\)-289,289\(\right\]\rbrack\)$,

Left-continuous at $289$, right-continuous at $-289$

$[-17,17]$,

Left-continuous at $-17$, right-continuous at $17$

$\(\left\[\lbrack\)-17,17\(\right\]\rbrack\)$,

Left-continuous at $17$, right-continuous at $-17$