Answer
a) $\lim\limits_{x \to 0^{-}}g(x) = 3$
b) $\lim\limits_{x \to 0^{+}}g(x) = 3$
c) $\lim\limits_{x \to 0}g(x) = 3$
d) $g(0) = 3$
e) $\lim\limits_{x \to -\infty}g(x) = +\infty$
f) $\lim\limits_{x \to +\infty}g(x) = +\infty$
Work Step by Step
a) As the graph of g(x) approaches x = 0 from the left, the y-value approaches 3.
b) As the graph of g(x) approaches x = 0 from the right, the y-value approaches 3.
c) Since the limit from the left and the limit from the right are equal, the limit as x goes to 0 of g(x) is 3.
d) The y-value at x = 0 of g(x) is 3.
e) As the x-value of g(x) gets smaller, the y-value increases without bound, so the limit as x goes to $-\infty$ of g(x) is $+\infty$.
f) As the x-value of g(x) gets larger, the y-value increases without bound, so the limit as x goes to $+\infty$ of g(x) is $+\infty$.
