Answer
a. True,
b. True,
c. False,
d. True,
e. True,
f. True,
g. False,
h. False,
i. False,
j. False,
k. True,
l. False,
Work Step by Step
Based on the graph given in the Exercise:
a. True, because when $x$ approaches $-1$ from the right-side, $f(x)\to 1$
b. True, because when $x$ approaches $0$ from the left-side, $f(x)\to 0$
c. False, because when $x$ approaches $0$ from the left-side, $f(x)\to 0$
d. True, because when $x$ approaches $0$ from the left or right-side, $f(x)\to 0$
e. True, because when $x$ approaches $0$ from the left and right-side, $f(x)\to 0$
f. True, because when $x$ approaches $0$ from the left and right-side, $f(x)\to 0$
g. False, because $lim_{x\to0}f(x)= 0$ while $f(0)=1$ is the function value at this point.
h. False, $lim_{x\to1}f(x)$ does not exist because the left and right limits are different.
i. False, $lim_{x\to1}f(x)$ does not exist because the left and right limits are different.
j. False, because when $x$ approaches $2$ from the left-side, $f(x)\to 0$
k. True, because we do not know the function to the left side of point $x=-1$
l. False, because we do not know the function to the right side of point $x=2$
