Graph each step function. See Examples 5 and 6 See Exercise 41 . Find the cost of a 20.75 -minut

step 1 The function F of X represents the cost of a call where X is the number of minutes, the length o

Graph each step function. See Examples 5 and 6 See Exercise...

Key Concepts

Step Function

A step function is a function that remains constant over specific intervals and then jumps abruptly to another constant value at specified breakpoints. It is used to model situations where changes occur in discrete steps rather than continuously.

Graphing Step Functions

Graphing step functions involves drawing horizontal line segments to represent periods where the function remains constant, with open or closed endpoints indicating whether the value at the breakpoint is included. This visual representation clearly shows the discrete jumps or discontinuities.

Piecewise Functions

Piecewise functions are defined by different expressions over various intervals of the domain. Step functions are a particular type of piecewise function where each piece is a constant value, making them useful for modeling scenarios with fixed rates over intervals.

Cost Function

A cost function, in contexts such as telephone billing, maps the duration of an activity (like a phone call) to the total cost incurred. Often, this is expressed as a step function where the cost increases in fixed increments after each interval, reflecting the billing system's structure.

Ceiling Function

The ceiling function rounds any non-integer value up to the next whole number. It is relevant in cost calculations, such as determining the billing time in minutes for a call, where partial minutes may be charged as a full minute.

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