Question

use the graph to determine the limit. (if an answer does not exist, enter dne.)
$c = - 3$
(a) $lim_{x
ightarrow c^{+}}f(x)=$
(b) $lim_{x
ightarrow c^{-}}f(x)=$
(c) $lim_{x
ightarrow c}f(x)=$
is the function continuous at $x = - 3$
yes
no

Explanation:

Step1: Right-hand limit as x→-3⁺

From graph, as x approaches -3 from right, f(x)→-3

Step2: Left-hand limit as x→-3⁻

From graph, as x approaches -3 from left, f(x)→-3

Step3: Overall limit as x→-3

Left and right limits equal (-3), so limit exists

Step4: Continuity at x=-3

Limit (-3) = f(-3)=-3, so continuous

Answer:

(a) -3
(b) -3
(c) -3
Yes