the graph below is the function f(x)\nselect all statements below that you agree with.\nnote: you may be…

the graph below is the function f(x)\nselect all statements below that you agree with.\nnote: you may be checking more than one box. no partial credit.\n□ f(2) is defined.\n□ lim_{x→2} f(x) exists.\n□ lim_{x→2} f(x)=f(2).\n□ the function is continuous at x = 2.\n□ the function is not continuous at x = 2.

the graph below is the function f(x)\nselect all statements below that you agree with.\nnote: you may be checking more than one box. no partial credit.\n□ f(2) is defined.\n□ lim_{x→2} f(x) exists.\n□ lim_{x→2} f(x)=f(2).\n□ the function is continuous at x = 2.\n□ the function is not continuous at x = 2.

Answer

Explanation:

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

The graph has a solid - dot at $x = 2$ with a $y$ - value. So $f(2)$ is defined.

Step2: Check if $\lim_{x\rightarrow2}f(x)$ exists

As $x$ approaches 2 from the left and the right, the function approaches the same $y$ - value (the open - dot value). So $\lim_{x\rightarrow2}f(x)$ exists.

Step3: Check if $\lim_{x\rightarrow2}f(x)=f(2)$

The value of the function at $x = 2$ (solid - dot) is different from the limit value (open - dot). So $\lim_{x\rightarrow2}f(x)\neq f(2)$.

Step4: Check continuity

Since $\lim_{x\rightarrow2}f(x)\neq f(2)$, the function is not continuous at $x = 2$.

Answer:

$f(2)$ is defined. $\lim_{x\rightarrow2}f(x)$ exists. The function is not continuous at $x = 2$.