Questions: Select the correct answer below: f(a) is not continuous at n=-3 because it is not defined at x=-3 f(x) is not continuous at x=-3 because lim x→1 f(x) does not exist. f(x) is not continuous at x=-3 because lim x→1 f(x) / f(-3) f(x) is continuous at x=-3

Select the correct answer below:
f(a) is not continuous at n=-3 because it is not defined at x=-3
f(x) is not continuous at x=-3 because lim x→1 f(x) does not exist.
f(x) is not continuous at x=-3 because lim x→1 f(x) / f(-3)
f(x) is continuous at x=-3

Transcript text: Select the correct answer below: $f(a)$ is not continuous at $n=-3$ because it is not defined at $x=-3$ $f(x)$ is not continuous at $x=-3$ because $\lim _{x \rightarrow 1} f(x)$ does not exist. $f(x)$ is not continuous at $x=-3$ because $\lim _{x \rightarrow 1} f(x) / f(-3)$ $f(x)$ is continueus at $x=-3$

Solution

Solution Steps

Step 1: Analyze the graph at x = -3

The graph shows a defined point at x = -3, which is part of the line segment existing for x < -3. The function value appears to be f(-3) = 2.

Step 2: Analyze the limit as x approaches -3

As x approaches -3 from the left, the function approaches 2. As x approaches -3 from the right, the function also approaches 2. Therefore, the limit as x approaches -3 exists and is equal to 2.

Step 3: Determine continuity

Since f(-3) = 2 and the limit as x approaches -3 is 2, the function is continuous at x = -3.