Final answer:
To write the function rule for each piece of a piecewise function, define the specific expressions and the conditions under which they apply. Each condition represents an interval over which the corresponding function expression is valid.
Step-by-step explanation:
To write the function rule for each piece of a piecewise function, we need to define multiple expressions, each representing a different function piece, along with the specific condition or interval where each piece is applicable. A piecewise function can be written as:The function rule for each piece of a piecewise function is specific to that piece.
For example, let's say we have a piecewise function defined as follows:f(x) = 2x for x < 0f(x) = x^2 for 0 <= x <= 3f(x) = 5 for x > 3In this case, the function rule for the first piece is f(x) = 2x, the function rule for the second piece is f(x) = x^2, and the function rule for the third piece is f(x) = 5.For example, if we have a piecewise function that is defined by 'x^2' when 'x < 0' and '2x+1' when 'x ≥ 0', we would write it as:Here, x^2 is the function rule for the piece where x is less than zero, and 2x+1 is the function rule for the piece where x is greater than or equal to zero.