Question

question answer all of the questions below about the function f(x) graphed below when x = -4. answer attempt 2 out of 2 ∞ -∞ dne undefined lim_{x→ - 4^{-}}f(x)= lim_{x→ - 4^{+}}f(x)= lim_{x→ - 4}f(x)= f(-4)=

Explanation:

Step1: Analyze left - hand limit

As \(x\) approaches \(-4\) from the left (\(x\to - 4^{-}\)), we look at the values of the function as \(x\) gets closer to \(-4\) from values less than \(-4\). Following the curve, we see that the \(y\) - value approaches \(0\). So, \(\lim_{x\to - 4^{-}}f(x)=0\).

Step2: Analyze right - hand limit

As \(x\) approaches \(-4\) from the right (\(x\to - 4^{+}\)), we look at the values of the function as \(x\) gets closer to \(-4\) from values greater than \(-4\). Following the curve, we see that the \(y\) - value approaches \(0\). So, \(\lim_{x\to - 4^{+}}f(x)=0\).

Step3: Analyze overall limit

Since \(\lim_{x\to - 4^{-}}f(x)=\lim_{x\to - 4^{+}}f(x) = 0\), then \(\lim_{x\to - 4}f(x)=0\).

Step4: Analyze function value

The function has a hole at \(x = - 4\), so \(f(-4)\) is undefined.

Answer:

\(\lim_{x\to - 4^{-}}f(x)=0\), \(\lim_{x\to - 4^{+}}f(x)=0\), \(\lim_{x\to - 4}f(x)=0\), \(f(-4)=\text{undefined}\)