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How to write piecewise functions for absolute values.

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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

}

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