Question

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