answer attempt 1 out of 2 dne undefined since lim_{x→0^ - }f(x)= and lim_{x→0^ + }f(x)=, it can be…

answer attempt 1 out of 2 dne undefined since lim_{x→0^ - }f(x)= and lim_{x→0^ + }f(x)=, it can be determined that lim_{x→0}f(x) exists and is equal to. furthermore, it can be seen that f(0)=. therefore, it can be stated that the function f(x) is at x = 0 because

answer attempt 1 out of 2 dne undefined since lim_{x→0^ - }f(x)= and lim_{x→0^ + }f(x)=, it can be determined that lim_{x→0}f(x) exists and is equal to. furthermore, it can be seen that f(0)=. therefore, it can be stated that the function f(x) is at x = 0 because

Answer

Explanation:

Step1: Find left - hand limit

As (x\to0^{-}), by observing the graph, we approach the value of the function from the left - hand side of (x = 0). The value of (y) approaches (2). So, (\lim_{x\to0^{-}}f(x)=2).

Step2: Find right - hand limit

As (x\to0^{+}), by observing the graph, we approach the value of the function from the right - hand side of (x = 0). The value of (y) approaches (2). So, (\lim_{x\to0^{+}}f(x)=2).

Step3: Determine the limit

Since (\lim_{x\to0^{-}}f(x)=\lim_{x\to0^{+}}f(x) = 2), then (\lim_{x\to0}f(x)=2).

Step4: Find the function value at (x = 0)

From the graph, the point on the function at (x = 0) has a (y) - value of (2). So, (f(0)=2).

Step5: Determine continuity

A function (y = f(x)) is continuous at (x=a) if (\lim_{x\to a}f(x)=f(a)). Here, since (\lim_{x\to0}f(x)=2) and (f(0)=2), the function (f(x)) is continuous at (x = 0).

Answer:

(\lim_{x\to0^{-}}f(x)=2), (\lim_{x\to0^{+}}f(x)=2), (\lim_{x\to0}f(x)=2), (f(0)=2), continuous