Here are the essential concepts you must grasp in order to answer the question correctly.
Function Notation
Function notation, such as ƒ(x), represents a relationship between an input (x) and an output (ƒ(x)). In this context, ƒ(x) describes the cost of mailing a letter based on its weight in ounces. Understanding how to interpret and evaluate functions is crucial for solving problems involving variable relationships.
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Piecewise Functions
Piecewise functions are defined by different expressions based on the input value. The cost function ƒ(x) includes a term that changes based on the weight of the letter, indicating that the cost may vary for different ranges of x. Recognizing how to work with piecewise functions is essential for accurately determining costs in this scenario.
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Evaluating Functions
Evaluating a function involves substituting a specific value for the variable to find the corresponding output. In this case, to find the cost for the first ounce, we need to evaluate ƒ(x) at x=1. This process is fundamental in algebra, as it allows us to derive specific results from general formulas.
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Evaluating Composed Functions