Question

the image shows a coordinate grid with a graph of a function. there is a question related to the functions behavior, likely about limits or continuity, with options including does not exist and a text box for input. (ocr text is limited due to image focus, but the main elements are the graph and related question prompts.)

Explanation:

Step1: Identify limit from left

As $x$ approaches $-3$ from the left ($x \to -3^-$), the graph approaches $-3$.

Step2: Identify limit from right

As $x$ approaches $-3$ from the right ($x \to -3^+$), the graph approaches $-3$.

Step3: Compare left/right limits

Since $\lim_{x \to -3^-} f(x) = \lim_{x \to -3^+} f(x) = -3$, the two-sided limit exists and equals this value.

Answer:

$-3$