determine whether the following function is continuous at a. use the continuity checklist to justify your…

determine whether the following function is continuous at a. use the continuity checklist to justify your answer. f(x)=√(x - 4); a = 2 select all that apply. a. the function is continuous at a = 2. b. the function is not continuous at a = 2 because f(2) is undefined. c. the function is not continuous at a = 2 because lim x→2 f(x) does not exist. d. the function is not continuous at a = 2 because lim x→2 f(x)≠f(2).

determine whether the following function is continuous at a. use the continuity checklist to justify your answer. f(x)=√(x - 4); a = 2 select all that apply. a. the function is continuous at a = 2. b. the function is not continuous at a = 2 because f(2) is undefined. c. the function is not continuous at a = 2 because lim x→2 f(x) does not exist. d. the function is not continuous at a = 2 because lim x→2 f(x)≠f(2).

Answer

Explanation:

Step1: Evaluate f(2)

Substitute x = 2 into f(x) = $\sqrt{x - 4}$. We get f(2)=$\sqrt{2 - 4}=\sqrt{- 2}$, which is undefined in the set of real - numbers.

Step2: Recall continuity conditions

For a function y = f(x) to be continuous at x = a, three conditions must be met: 1. f(a) is defined. 2. $\lim_{x\rightarrow a}f(x)$ exists. 3. $\lim_{x\rightarrow a}f(x)=f(a)$. Since f(2) is undefined, the function is not continuous at x = 2.

Answer:

B. The function is not continuous at a = 2 because f(2) is undefined.