How do you write the original function as a piecewise function #y= -3* abs(x+1)+4#?

1 Answer
Jul 6, 2018

Answer:

#f(x)={(3x+7, color(white)("XX"),x <= -1),(-3x+1,,x > -1):}#

Explanation:

Given: #y = -3 * |x + 1| + 4#

The absolute value function always has a positive answer. The quantity inside the absolute value can be both positive or negative. This means there are two possible equations:

#y = -3(x + 1) + 4 = -3x -3 + 4#

# y = -3x + 1 #

#y = -3 (-1)(x + 1) + 4 = 3(x+1) + 4#

#y = 3x + 3 + 4#

#y = 3x + 7#

The vertex of the absolute value occurs when the quantity in the absolute value #= 0#:

#x + 1 = 0 => **x = -1** #

Piecewise function is

#f(x)={(3x+7, color(white)("XX"),x <= -1),(-3x+1,,x > -1):}#