The graph provided seems to represent a piecewise function based on the red line segments and points shown. Here's how we can analyze the function step by step: Left Line Segment: The first part of the graph (for x ≤ 1 x≤1) is a straight line with a negative slope. It starts from approximately ( (x = -2, y = 4) ) and passes through ( (x = 1, y = 0) ). Using these two points, we can calculate the slope m m of the line: m = 0 − 4 1 − ( − 2 ) = − 4 3 = − 4 3 m= 1−(−2) 0−4 ​ = 3 −4 ​ =− 3 4 ​ Using the slope-intercept form y = m x + b y=mx+b, where m = − 4 3 m=− 3 4 ​ and the point ( (1, 0) ) to find b b (the y-intercept): 0 = − 4 3 ( 1 ) + b    ⟹    b = 4 3 0=− 3 4 ​ (1)+b⟹b= 3 4 ​ So, for x ≤ 1 x≤1, the equation of the line is: y = − 4 3 x + 4 3 y=− 3 4 ​ x+ 3 4 ​ Right Segment: The second part of the graph is a horizontal line at y = 2 y=2 starting from x = 2 x=2 (closed dot at ( (2, 2) )) and ending at x = 4 x=4 (open dot at ( (4, 2) )). Thus, for 2 ≤ x < 4 2≤x<4, the equation is: y = 2 y=2