Final Answer:
The statement given "Intervals for piecewise functions are usually written in set-builder notation." is true because set-builder notation is better than interval notation because it is more concise and easier to read.
Step-by-step explanation:
Intervals for piecewise functions are usually written in set-builder notation. This is because set-builder notation allows us to specify the range of values for each piecewise definition of the function. For example, the following piecewise function:
f(x) = {
2x if x < 0
-x if x ≥ 0
}
can be represented using interval notation as:
f(x) = x ∈ (−∞, 0) ∪ -x
In this way, we can clearly define the different domains and ranges of each piecewise definition of the function.