Questions: Answer all of the questions below about the function f(x) graphed below when x=3. lim x → 3⁻ f(x)= □ lim x → 3⁺ f(x)= □ lim x → 3 f(x)= □ f(3)= □

Transcript text: Answer all of the questions below about the function $f(x)$ graphed below when $x=3$. $\lim _{x \rightarrow 3^{-}} f(x)=$ $\square$ $\lim _{x \rightarrow 3^{+}} f(x)=$ $\square$ $\lim _{x \rightarrow 3} f(x)=$ $\square$ $f(3)=$ $\square$

Solution

Solution Steps

To find the values of the limits and the function at x=3, we need to analyze the behavior of the function as x approaches 3 from the left and from the right. We also need to determine the value of the function at x=3.

Step 1: Determine the Limits

The limit from the left as $ x $ approaches 3 is 6, and the limit from the right as $ x $ approaches 3 is also 6. Therefore, the limit as $ x $ approaches 3 is $ \boxed{6} $.

Step 2: Calculate the Value of the Function at $ x = 3 $

Substitute $ x = 3 $ into the function $ f(x) = \frac{x^2 - 9}{x - 3} $ results in an undefined value (nan) due to division by zero. Hence, the value of the function at $ x = 3 $ is $ \boxed{DNE} $.