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

1 Answer
marfre
Jul 6, 2018

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):}

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