Question

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

Answer 1

`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):}`