Question

score on last try: 0 of 1 pt. see details for more.get a similar question you can retry this question belowthe graph below is the function $f(x)$select all statements below that you agree with.note: you may be checking more than one box. no partial credit.$square f(2)$ is defined.$square lim_{x \to 2} f(x)$ exists.$square lim_{x \to 2} f(x) = f(2)$.$square$ the function is continuous at $x = 2$.$square$ the function is not continuous at $x = 2$.

Explanation:

Step1: Check if $f(2)$ is defined

Look at the graph: at $x=2$, there is a filled point at $y=-4$, so $f(2)=-4$, meaning it is defined.

Step2: Check if $\lim_{x \to 2} f(x)$ exists

Observe the left-hand limit (as $x$ approaches 2 from the left, the graph approaches $y=2$) and the right-hand limit (as $x$ approaches 2 from the right, the graph approaches $y=2$). Since left and right limits are equal, $\lim_{x \to 2} f(x)=2$, so the limit exists.

Step3: Check if $\lim_{x \to 2} f(x) = f(2)$

We have $\lim_{x \to 2} f(x)=2$ and $f(2)=-4$. $2
eq -4$, so this equality does not hold.

Step4: Check continuity at $x=2$

A function is continuous at $x=a$ if $\lim_{x \to a} f(x) = f(a)$. Since this equality fails here, the function is not continuous at $x=2$.

Answer:

• $f(2)$ is defined.
• $\lim_{x \to 2} f(x)$ exists.
• The function is not continuous at $x = 2$.