 The 2022 domestic postage rate for firstclass letters weighing 3.5 oz or less is 60 cents for the first
ounce (or less), plus 24 cents for each additional ounce (or
part of an ounce). Express the postage P as a piecewisedefined function of the weight x of a letter, with 0  x  3.5,
and sketch a graph of this function.

The graph above represents the postage cost as a function of the weight of a letter. As you can see, the graph is a step function with jumps at \( x = 1 \), \( x = 2 \), and \( x = 3 \), where the postage increases by 24 cents at each step.

Do you want further details or have any questions?

Here are 5 related questions to deepen your understanding:
1. How would the postage change if the rate for additional ounces increased to 30 cents?
2. What happens to the function if the weight limit increases to 4 ounces?
3. How would you express this function if the base rate increased to 65 cents for the first ounce?
4. Can you modify this function for international postage, where the rates increase differently?
5. How can this piecewise function be written using a summation notation?

**Tip:** When dealing with piecewise functions, always check the boundary conditions for accuracy (e.g., check the transition points where the function changes).

The 2022 domestic postage rate for first-class letters weighing 3.5 oz or less is 60 cents for the first ounce (or less), plus 24 cents for each additional ounce (or part of an ounce). Express the postage P as a piecewise-defined function of the weight x of a letter, with 0 < x ≤ 3.5, and sketch a graph of this function.

This guide explains how to express the 2022 domestic postage rate for first-class letters weighing up to 3.5 oz as a piecewise-defined function. Learn the step-by-step breakdown for calculating postage, including the base rate of 60 cents and an additional 24 cents for each extra ounce.

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