The image contains a graph of a piecewise function, and it asks which of the given functions best represents the graph.

Let me analyze the graph to determine the appropriate function. I will examine the slopes and intercepts of the lines on the graph to match them to the given choices.

Afterward, I will provide the correct function and reasoning. PIL import Image

Load the image to analyze

img_path = '/mnt/data/1741191688557sca14amc.jpg' img = Image.open(img_path)

Display the image

img.show()I have displayed the image, and I will now analyze the graph. Based on the graph, I will identify key features like slope, intercepts, and the boundaries for the piecewise function. I'll compare these with the provided options.

Please give me a moment to analyze the graph.Upon analyzing the graph, it appears that there are two line segments with different slopes in different intervals:

• The first segment has a slope of $\frac{1}{3}$ and appears to be in the interval $-5 < x < 0$.
• The second segment has a slope of $\frac{1}{3}$ and seems to be in the interval $0 \leq x \leq 3$, with a different constant term.

Given these observations, the correct function should match these slope values and intervals. The appropriate function based on these characteristics is: