Question

The absolute value function in the graph above is written as a piecewise

function with a dividing point at x = 0. This is because |0|= ___?

Answer 1

First, the absolute value is a function that always has a positive output.

We can write the absolute value function as:

IxI = x if x > 0 (x is positive)

IxI = - x if x < 0. (x is negative)

But what happens if x = 0?

this is because 0 is equal to +0 and -0, then we have that:

I0I = 0 = +0 = -0.

So we can actually write the absolute value function as:

IxI = x if x ≥ 0 (x is positive)

IxI = - x if x ≤ 0. (x is negative)