Complete the equation for the piecewise function graphed bel

Complete the equation for the piecewise function graphed below. f(x) = {_________ if - 6 lessthanorequalto x lessthanorequalto -2 {___________ if -2

Solution

for -6 <= x <= -2

(-6, 5) to (-2, -1) ========> (y - 5) = [(-1-5)/(-2+6)]*(x + 6)

y - 5 = -3/2*(x + 6)

2y -10 = -3x - 18 =======> 3x + 2y = -8 for -6 <= x <= -2

ii) for -2 < x <= 1

(-2, -2) to (1, -2) ========> (y + 2) = [(-2 + 2)/(1+2)]*(x + 2)

y = -2 for -2 < x <= 1

iii) for 1 < x <= 6

(1, -3) to (6, 2) ========> (y + 3) = [(2 + 3)/(6 - 1)]*(x - 1)

y + 3 = x - 1

x - y = 2 for 1 < x <= 6