Question

use the graph to evaluate the limit. find lim f(x) and lim f(x) x→(-1)^- x→(-1)^+ -7; -5 -5; -2 -2; -7 -7; -2

Explanation:

Step1: Analyze left - hand limit

As \(x\) approaches \(- 1\) from the left (\(x\to(-1)^{-}\)), we look at the part of the graph to the left of \(x =-1\). Following the curve on the left - hand side of \(x=-1\), the \(y\) - value approaches \(-7\).

Step2: Analyze right - hand limit

As \(x\) approaches \(-1\) from the right (\(x\to(-1)^{+}\)), we look at the part of the graph to the right of \(x = - 1\). Following the curve on the right - hand side of \(x=-1\), the \(y\) - value approaches \(-2\).

Answer:

D. \(-7; - 2\)