Final answer:
To write a piecewise function for absolute values, consider different cases based on the input value. When x is positive or zero, the function is equal to x. When x is negative, the function is equal to the negation of x.
Step-by-step explanation:
To write a piecewise function for absolute values, you need to consider different cases based on the input value. Let's define a function f(x) using absolute value:
f(x) = |x|
When x is positive or zero, f(x) is equal to x. So, we can write:
f(x) = x, for x ≥ 0
When x is negative, f(x) is equal to the negation of x. So, we can write:
f(x) = -x, for x < 0
This gives us the piecewise function:
f(x) = {
x, for x ≥ 0
-x, for x < 0
}