A verbal description of a function is given. Find a....

A verbal description of a function is given. Find
a. algebraic,
b. numerical, and
c. graphical representations for the function.
To evaluate $f(x)$, divide the input by 3 and add $\frac{2}{3}$ to the result.

Key Concepts

Function

A function is a relation that associates each element in a set (called the domain) with exactly one element in another set (possibly the same set, called the range). It serves as a rule that assigns to every input a unique output and is a foundation for understanding various mathematical processes and models.

Verbal Representation

A verbal representation describes the behavior of a function using words. This method emphasizes explaining the process or rule by which each input is transformed into an output and is useful for conceptual understanding and communicating mathematical ideas in a non-symbolic format.

Algebraic Representation

An algebraic representation expresses a function using symbols and mathematical operations, typically in the form of an equation. This formal representation enables precise computation and analysis and is central to solving problems, proving properties, and developing deeper insights in mathematics.

Numerical Representation

A numerical representation of a function involves listing the input-output pairs, often in the form of a table. This method allows for the examination of specific values, estimation of behavior, and the identification of patterns, making it a practical tool for understanding and approximating the properties of functions.

Graphical Representation

A graphical representation depicts a function visually by plotting its input-output pairs on a coordinate system. This approach provides an intuitive understanding of the function’s behavior, including aspects such as trends, continuity, and intercepts, and is especially helpful in analyzing how changes in variables influence outcomes.

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