Answer
a: $1$;
b: $1$
c: $1$
d: $0$
e: $0$
f: $0$
g: $4$
h: $2$
i: DNE
Work Step by Step
a: We look to when $x$ approaches $-1$ from the left side of the graph, and from this perspective, the $y$-value approaches $1$.
b: We look to when $x$ approaches $-1$ from the right side of the graph, and from this perspective, the $y$-value approaches $1$.
c: Since $\displaystyle\lim_{x\to-1^-} f(x) = \displaystyle\lim_{x\to-1^+} f(x)$, $\displaystyle\lim_{x\to-1} f(x)$ exists, and it is also $1$.
d: We look to when $x$ approaches $0$ from the left side of the graph, and from this perspective, the $y$-value approaches $0$.
e: We look to when $x$ approaches $0$ from the right side of the graph, and from this perspective, the $y$-value approaches $0$.
f: Since $\displaystyle\lim_{x\to 0^-} f(x) = \displaystyle\lim_{x\to0^+} f(x)$, $\displaystyle\lim_{x\to0} f(x)$ exists, and it is also $0$.
g: We look to when $x$ approaches $2$ from the left side of the graph, and from this perspective, the $y$-value approaches $4$.
h: We look to when x approaches $2$ from the right side of the graph, and from this perspective, the $y$-value approaches $2$.
i: Since $\displaystyle\lim_{x\to2^-} f(x)$ $\ne \displaystyle\lim_{x\to2^+} f(x)$, $\displaystyle\lim_{x\to2} f(x)$ does not exist.
