Questions: Select all statements below that you agree with. Note: You may be checking more than one box. No partial credit. f(2) is defined. lim x -> 2 f(x) exists. lim x -> 2 f(x) = f(2). The function is continuous at x=2. The function is not continuous at x=2.

Select all statements below that you agree with.
Note: You may be checking more than one box. No partial credit.
f(2) is defined.
lim x -> 2 f(x) exists.
lim x -> 2 f(x) = f(2).
The function is continuous at x=2.
The function is not continuous at x=2.

Transcript text: Select all statements below that you agree with. Note: You may be checking more than one box. No partial credit. $f(2)$ is defined. $\lim _{x \rightarrow 2} f(x)$ exists. $\lim _{x \rightarrow 2} f(x)=f(2)$. The function is continuous at $x=2$. The function is not continuous at $x=2$.

Solution

Solution Steps

Step 1: Determine if f(2) is defined

The graph shows a solid dot at x = 2, at the point (2,2). This means f(2) = 2. Thus, f(2) is defined.

Step 2: Determine if the limit of f(x) as x approaches 2 exists.

As x approaches 2 from the left, f(x) approaches 2. As x approaches 2 from the right, f(x) approaches 0. Since the left-hand limit and the right-hand limit are not equal, the limit of f(x) as x approaches 2 does not exist.

Step 3: Determine if the limit of f(x) as x approaches 2 is equal to f(2).

Since the limit of f(x) as x approaches 2 does not exist, it cannot be equal to f(2).