Postage Rates In 2013 , the retail flat rate in dollars for...

Postage Rates In 2013 , the retail flat rate in dollars for first-class mail weighing up to 5 ounces could be computed by the piecewise constant function $f,$ where $x$ is the number of ounces. $$f(x)=\left\{\begin{array}{ll} 0.92 & \text { if } 0<x \leq 1 \\ 1.12 & \text { if } 1<x \leq 2 \\ 1.32 & \text { if } 2<x \leq 3 \\ 1.52 & \text { if } 3<x \leq 4 \\ 1.72 & \text { if } 4<x \leq 5 \end{array}\right.$$ A.Evaluate $f(1.5)$ and $f(3) .$ Interpret your results. B. Sketch a graph of $f .$ What is its domain? What is its range?

Postage Rates In 2013 , the retail flat rate in dollars for first-class mail weighing up to 5 ounces could be computed by the piecewise constant function $f,$ where $x$ is the number of ounces.
$$f(x)=\left\{\begin{array}{ll} 0.92 & \text { if } 0<x \leq 1 \\ 1.12 & \text { if } 1<x \leq 2 \\ 1.32 & \text { if } 2<x \leq 3 \\ 1.52 & \text { if } 3<x \leq 4 \\ 1.72 & \text { if } 4<x \leq 5 \end{array}\right.$$
A.Evaluate $f(1.5)$ and $f(3) .$ Interpret your results.
B. Sketch a graph of $f .$ What is its domain? What is its range?

Key Concepts

Piecewise Function

A piecewise function is defined by different formulas for different parts of its domain. Each segment of the domain uses a specific expression, allowing the function to model situations with distinct conditions or rules over various intervals.

Function Evaluation

Function evaluation involves substituting a specific value into the function's expression to determine the corresponding output. In the context of a piecewise function, this means identifying which interval the input value belongs to and using the corresponding formula.

Domain

The domain of a function is the complete set of input values for which the function is defined. For piecewise functions, the domain is determined by the combined intervals of each piece, ensuring that every input has an associated output.

Range

The range of a function is the set of all possible output values produced by the function. In piecewise functions, the range is derived from the outputs of each individual piece, representing all potential results of evaluating the function.

Graphing Piecewise Functions

Graphing a piecewise function involves plotting each segment over its corresponding interval. For piecewise constant functions, this typically results in a step-like graph where the function value remains constant within each interval, and discontinuities may occur at the endpoints of the intervals.

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