Answer :
Answer:
Option (1)
Step-by-step explanation:
From the graph of the piecewise function,
There are two pieces of the function,
1). Segment (1) having x < 0
2). Segment (2) having x ≥ 0
Segment (1),
Segment starts with a hollow circle at x = 0 and passes through two points (0, 1) and (-2, 2)
Slope of the segment = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
= [tex]\frac{2-1}{-2-0}[/tex]
= [tex]-\frac{1}{2}[/tex]
Equation of the segment passing through (-2, 2) with slope = [tex]-\frac{1}{2}[/tex],
[tex]y-y'=m(x-x')[/tex]
[tex]y-2=-\frac{1}{2}(x+2)[/tex]
[tex]y=-\frac{1}{2}x-1+2[/tex]
[tex]y=-\frac{1}{2}x+1[/tex]
[tex]y=-0.5x+1[/tex] For x < 0
Segment (2),
Segment starts with a solid circle at x = 0 and passes through (0, -2) and (2,2)
Slope of the segment = [tex]\frac{2+2}{2-0}[/tex]
= 2
Equation of the segment passing through (0, -2) and slope = 2,
y - y' = m(x - x')
y + 2 = 2(x - 0)
y = 2x - 2 For x ≥ 0
Therefore, Option (1) will be the correct option.