question 8 find lim_{x→ - 4} f(x) the limit does not exist - 3 0

Explanation:

Step1: Analyze left - hand limit

As (x) approaches (- 4) from the left side ((x\to - 4^{-})), we look at the values of (y = f(x)) on the graph for (x) values slightly less than (-4). Following the curve, the (y) - value approaches (-3).

Step2: Analyze right - hand limit

As (x) approaches (- 4) from the right side ((x\to - 4^{+})), we look at the values of (y = f(x)) on the graph for (x) values slightly greater than (-4). Following the curve, the (y) - value also approaches (-3).

Step3: Determine the limit

Since (\lim_{x\to - 4^{-}}f(x)=\lim_{x\to - 4^{+}}f(x)=- 3), then (\lim_{x\to - 4}f(x)=-3).

Answer:

-3