Question

which of the statements a through i about the function y = f(x) graphed here are true, and which are false?
a. the statement lim f(x) does not exist is
x→2

Explanation:

Step1: Recall the definition of the limit

The limit of a function \(y = f(x)\) as \(x\to a\) exists if \(\lim_{x\to a^{-}}f(x)=\lim_{x\to a^{+}}f(x)\).

Step2: Analyze the left - hand limit and right - hand limit as \(x\to2\)

As \(x\) approaches \(2\) from the left (\(x\to2^{-}\)), we look at the part of the graph for \(x < 2\). As \(x\) approaches \(2\) from the right (\(x\to2^{+}\)), we look at the part of the graph for \(x>2\).
From the graph, \(\lim_{x\to2^{-}}f(x)
eq\lim_{x\to2^{+}}f(x)\)

Answer:

True