use the graph to find the following limits and function value. a. lim f(x) x→3⁻ b. lim f(x) x→3⁺ c. lim f(x)…

Explanation:

Step1: Analyze left - hand limit

As (x) approaches (3) from the left ((x\to3^{-})), we look at the part of the graph where (x) values are less than (3) and getting closer to (3). Following the curve of the function for (x < 3) and approaching (x = 3), we see that the (y) - value approaches (1).

Step2: Analyze right - hand limit

As (x) approaches (3) from the right ((x\to3^{+})), we look at the part of the graph where (x) values are greater than (3) and getting closer to (3). Following the curve of the function for (x>3) and approaching (x = 3), we see that the (y) - value approaches (- 1).

Step3: Analyze overall limit

The overall limit (\lim_{x\to3}f(x)) exists if and only if (\lim_{x\to3^{-}}f(x)=\lim_{x\to3^{+}}f(x)). Since (\lim_{x\to3^{-}}f(x) = 1) and (\lim_{x\to3^{+}}f(x)=-1), (\lim_{x\to3}f(x)) does not exist.

Step4: Find function value

To find (f(3)), we look at the point on the graph where (x = 3). The filled - in dot at (x = 3) has a (y) - value of (1).

Answer:

a. A. (\lim_{x\to3^{-}}f(x)=1) b. (\lim_{x\to3^{+}}f(x)= - 1) c. B. The limit does not exist. d. (f(3)=1)