the graph of a function is given. use the graph to find the indicated limit and function value, or state…

Explanation:

Step1: Analyze left - hand limit

As (x) approaches (1) from the left ((x\to1^{-})), the (y) - values approach (1).

Step2: Analyze right - hand limit

As (x) approaches (1) from the right ((x\to1^{+})), the (y) - values approach (1). Since the left - hand limit and the right - hand limit are equal, (\lim_{x\to1}f(x)=1).

Step3: Find function value

To find (f(1)), we look at the solid dot on the graph at (x = 1). The (y) - value at the solid dot when (x = 1) is (1), so (f(1)=1).

Answer:

a. (\lim_{x\to1}f(x)=1) b. (f(1)=1)