Question

answer all of the questions below about the function f(x) graphed below when x = -6.

answer attempt 1 out of 2
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\lim_{x \to -6^{-}} f(x) = \square
\lim_{x \to -6^{+}} f(x) = \square
\lim_{x \to -6} f(x) = \square
f(-6) = \square

Explanation:

Step1: Analyze the left - hand limit

As \(x\) approaches \(-6\) from the left (\(x\to - 6^{-}\)), we look at the behavior of the function values. The function approaches \(-4\). So, \(\lim_{x\to - 6^{-}}f(x)=-4\)

Step2: Analyze the right - hand limit

As \(x\) approaches \(-6\) from the right (\(x\to - 6^{+}\)), we look at the behavior of the function values. The function approaches \(-4\). So, \(\lim_{x\to - 6^{+}}f(x)=-4\)

Step3: Analyze the two - sided limit

Since \(\lim_{x\to - 6^{-}}f(x)=\lim_{x\to - 6^{+}}f(x)\), then \(\lim_{x\to - 6}f(x)=-4\)

Step4: Find the function value at \(x = - 6\)

The point on the graph at \(x=-6\) has a \(y\) - value of \(-4\). So, \(f(-6)=-4\)

Answer:

\(\lim_{x\to - 6^{-}}f(x)=-4\), \(\lim_{x\to - 6^{+}}f(x)=-4\), \(\lim_{x\to - 6}f(x)=-4\), \(f(-6)=-4\)