## Thomas' Calculus 13th Edition

$a.\quad$yes $b.\quad$yes $c.\quad$yes $d.\quad$yes
The graph of f(x) contains points $(x,f(x))$, where x belongs to the domain of f. $a.$ The point $(-1,0)$ belongs to the graph of f, so $f(-1)=0$ ( $f(-1)$ exists) $b.$ As x approaches the value $-1$ from the right, f(x) approaches $0$. The right-sided limit exists, $\displaystyle \lim_{x\rightarrow 1^{+}}f(x)=0$, $c.$ $\displaystyle \lim_{x\rightarrow 1^{+}}f(x)=0$= $f(-1)$ (they are equal) $d.$ The domain of f contains the half-closed interval $[-1,0)$. The result of (c) implies that f is right-continuous at the left (closed) border, (see the first definitions of the section, and the discussion below them, referring to continuity over closed and half-closed intervals). So we say that f is continuous at $x=-1$.