question answer all of the questions below about the function f(x) graphed below when x = -4. answer attempt…

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)=

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)=

Answer

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})