answer attempt 1 out of 2\n∞ -∞ dne undefined\nlim_{x→ - 6^{-}}f(x)= \nlim_{x→ - 6^{+}}f(x)= \nlim_{x→…
answer attempt 1 out of 2\n∞ -∞ dne undefined\nlim_{x→ - 6^{-}}f(x)= \nlim_{x→ - 6^{+}}f(x)= \nlim_{x→ - 6}f(x)= \nf(-6)= \nsubmit answer
Answer
Explanation:
Step1: Analyze left - hand limit
As (x) approaches (-6) from the left ((x\to - 6^{-})), looking at the graph, the (y) - value approaches (-2). So (\lim_{x\to - 6^{-}}f(x)=-2).
Step2: Analyze right - hand limit
As (x) approaches (-6) from the right ((x\to - 6^{+})), from the graph, the (y) - value approaches (-3). So (\lim_{x\to - 6^{+}}f(x)=-3).
Step3: Analyze overall limit
Since (\lim_{x\to - 6^{-}}f(x)\neq\lim_{x\to - 6^{+}}f(x)), (\lim_{x\to - 6}f(x)) does not exist (DNE).
Step4: Analyze function value
The open - circle at (x = - 6) means the function is not defined at (x=-6), so (f(-6)) is undefined.
Answer:
(\lim_{x\to - 6^{-}}f(x)=-2), (\lim_{x\to - 6^{+}}f(x)=-3), (\lim_{x\to - 6}f(x)=\text{DNE}), (f(-6)=\text{undefined})