Use the graph of $f\(\left\)(x\(\right\))$ to determine if the function is continuous or discontinuous at $x=c$.
$c=-2$

• A. Continuous
• B. Discontinuous

Answer: (A)

Verified step by step guidance

1. To determine if the function f(x) is continuous at x = -2, we need to check three conditions: the function must be defined at x = -2, the limit of the function as x approaches -2 must exist, and the limit must equal the function value at x = -2.
2. First, check if f(x) is defined at x = -2. Look at the graph and see if there is a point at x = -2. In the graph, there is a solid dot at x = -2, indicating that f(-2) is defined.
3. Next, determine the limit of f(x) as x approaches -2 from both sides. Observe the graph to see if the function approaches the same value from the left and right as x approaches -2. The graph shows that the function approaches the same value from both sides.
4. Compare the limit of f(x) as x approaches -2 with the value of f(-2). Since the limit from both sides equals the value of the function at x = -2, the function is continuous at this point.
5. Conclude that f(x) is continuous at x = -2 because all three conditions for continuity are satisfied: the function is defined at x = -2, the limit exists, and the limit equals the function value.