-abs(x)+2

Input

-abs(x) + 2

Plot

Plot
Plot

Alternate form assuming x>0

2 - x

Alternate form assuming x is real

2 - sqrt(x^2)

Roots

x = 2 e^(i n), n element R

Integer root

x = ± 2

Properties as a real function

Domain

R (all real numbers)

Range

{y element R : y<=2}

Parity

even

Derivative

d/dx(-abs(x) + 2) = -x/abs(x) (assuming a function from reals to reals)

Indefinite integral assuming all variables are real

integral(-abs(x) + 2) dx = -1/2 x (x sgn(x) - 4) + constant

Global maximum

max{-abs(x) + 2} = 2 at x = 0

Alternative representation

-abs(x) + 2 = -x/sgn(x) + 2 for x!=0
-abs(x) + 2 = 2 - sqrt(x x^*)
-abs(x) + 2 = 2 - x/e^(i arg(x))
More information »

Definite integral

integral_(-2)^2 (2 - abs(x)) dx = 4
POWERED BY THE WOLFRAM LANGUAGE