Answer:
Option C.
Step-by-step explanation:
Slope of the line passing through (1, 1) and (0, 2)
m = [tex]\frac{y-y'}{x-x'}[/tex]
m = [tex]\frac{2-1}{0-1}[/tex]
m = -1
Equation of the line passing through point (1, 1) and slope = -1,
y - y' = m(x - x')
y - 1 = (-1)(x - 1)
y - 1 = -x + 1
y = -x + 2
This piece of function is true for x ≤ 1
Similarly, slope of the line passing through two points (1, -1) and (2, -3),
m' = [tex]\frac{-3+1}{2-1}[/tex]
= -2
Equation of the line passing through (1, -1) and slope = -2
y + 1 = (-2)(x - 1)
y + 1 = -2x + 2
y = -2x + 1
This piece of function is true for x > 1
Therefore, Option C. will be the answer.
