Question

the cost of mailing a first-class letter is $0.46 for the first ounce and $0.20 for each additional ounce or portion of an ounce. the letter y represents the total cost for mailing a letter that weighs x ounces. which type of function model would be appropriate for this situation?
absolute value function linear function step function square root function

Explanation:

Step1: Analyze the Cost Structure

The cost has a fixed part (\$0.46 for the first ounce) and a variable part (\$0.20 for each additional ounce or portion of an ounce). For example, if a letter weighs 1.1 ounces, it's treated as 2 ounces (since we pay for each additional portion of an ounce). So the cost "steps" up at each whole ounce increment.

Step2: Evaluate Function Types

• Absolute value function: Models distance or magnitude, not step - like cost with portioned ounces.
• Linear function: A linear function has a constant rate of change, but here the cost changes in steps (e.g., 1 - 2 ounces: cost is \$0.46+\$0.20, 2 - 3 ounces: \$0.46 + 2*\$0.20, etc., but even a fraction of an ounce in the range increases the cost by a step).
• Step function: A step function is a piece - wise constant function where the function value changes at distinct points (here, at each ounce mark). This matches the cost structure as we pay for each additional ounce or portion.
• Square root function: Models relationships with square - root dependence, not cost per ounce with portions.

Answer:

step function