Absolute value

The parent function of absolute value functions is f(x) = |x|. It is an even function that has a sharp turn at the bottom. The graph of this function is:

The absolute value function can also be described as a piecewise function:

f(x) =
-x,   x < 0
0,  x = 0
x,  x > 0

To transform the absolute value function, the general form of function transformations can be applied:

f(x) = a|b(x + c)| + d

See also function transformations, piecewise functions.