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The rules that define the graphed function are y = x + 2 and y = 5 Therefore, the graph will consist of three distinct sections as defined. These represent a piecewise function where the first line has a slope of 1 and the second is a constant horizontal line at y = 5

Therefore, the correct option is y = x + 2 Each segment is represented with careful attention to whether endpoints are included based on the conditions The general form of the equation for a line is given by

Y = mx + b where

Each segment of the graph corresponds to a specific mathematical rule based on its domain This helps clarify the overall behavior of the function across its entire range. To define the function graphed, identify key points on the graph, determine the type of function, analyze any transformations, and consider any asymptotes Finally, combine these observations to write an equation that represents the function

This structured approach will help accurately define the function based on its graphical representation. To solve the equation x2 − 4x + 1 = 0, we utilize the quadratic formula resulting in the solutions x = 2+ 3 and x = 2 − 3. The line y = x + 2 has a slope of 1 passing through (0, 2), while y = 5 is a horizontal line Both lines signify different behaviors of the function at varying intervals.

The function graphed may be identified by analyzing its slope and intercepts, possibly expressed through linear or horizontal equations

Key characteristics like the nature of the line (linear, horizontal, or curved) aid in defining the function Observing specific points can further refine the rules governing the function. To determine the function rule that describes the graph, we start by looking for patterns in the graph's sections If the graph consists of straight segments, these typically indicate linear functions.

The function is composed of three segments A linear segment for x <−2, a constant segment from −2 to 3, and another linear segment for x> 3

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