. Determine whether each function is continuous or discontinuous. A. First class postage, as a function of weight. (1 Point)

Determining Continuity of Functions

1. Break Down the Problem

   • We need to analyze the function that describes first-class postage as a function of weight. Specifically, we will consider how the postage rate changes as the weight of the mail increases.

2. Relevant Concepts

   • A function is continuous if there are no abrupt changes, jumps, or breaks in the function for all input values within its domain. For postage rates, we can typically reference a fee schedule that specifies rates at different weight intervals.

3. Analysis and Detail

   • The postage rates for first-class mail may be structured in tiers. For instance, if the weight increases continuously from 0 to a certain limit, the cost might increase gradually until a specific weight threshold is met. At that point, the cost jumps to the next tier:
     • Example:
       • For weights from 0 to 1 ounce: $0.55
       • From 1 ounce to 2 ounces: $0.70
       • The transition from 1 ounce to 2 ounces represents a jump, indicating a discontinuity at this weight.

4. Verify and Summarize

   • If there are specific thresholds (like weight limits) where the cost changes in a non-continuous manner, the function is discontinuous at those points. In this case, the function is likely to be discontinuous at weight thresholds, making it a piecewise function where gaps exist.

Final Answer

The function representing first-class postage as a function of weight is discontinuous at the threshold weights where the postage rate increases to the next tier.