the cost of mailing a first - class letter is $0.46 for the first ounce and $0.20 for each additional ounce…

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? step function square root function absolute value function linear function

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? step function square root function absolute value function linear function

Answer

Explanation:

Step1: Analyze the cost structure

The cost has a fixed part ($0.46 for the first ounce) and then an additional cost ($0.20 per additional ounce or portion). This is similar to a step - like behavior. For example, if (x = 1) ounce, (y=0.46); if (1\lt x\leq2), (y = 0.46+0.20); if (2\lt x\leq3), (y=0.46 + 0.20\times2) and so on.

Step2: Recall function definitions

  • A step function (also known as a piece - wise constant function) has a graph that is a series of horizontal line segments.
  • A square root function is of the form (y = a\sqrt{x}+b).
  • An absolute value function is of the form (y=a|x - h|+k).
  • A linear function is of the form (y = mx + b) (a straight - line graph).

Since the cost changes in discrete steps based on the weight intervals of the letter, the step - function model is appropriate.

Answer:

step function