Final answer:
The functionally defined logical or arithmetic manipulation of data is the process of performing operations on data following algorithms in a computer program. Understanding functions, manipulating equations, and interpreting graphs are fundamentals to this process, which is tested against mathematical models to ensure accuracy and reliability.
Step-by-step explanation:
The functionally defined logical or arithmetic manipulation of data refers to the operations carried out on data by a computer that follow the algorithms written within a computer program. These operations can be arithmetic, such as addition, subtraction, multiplication, and division, or logical operations like AND, OR, and NOT. In order to understand these concepts, it's important to learn what a function is, how to interpret and manipulate equations, and how to read and manipulate graphs.
For example, in a mathematical model, a function might take input data and produce an output according to a set rule or formula. This is essential in fields such as computer science and engineering where manipulating data functionally ensures the correct execution of programs and algorithms. The mathematical model of an operation should be carefully constructed and tested to ensure it employs the appropriate science and mathematics principles.
The ability to work these problems out step by step is crucial, often using methods described in the 'Work It Out' feature. This methodical approach helps to confirm the accuracy of computations and the correctness of the logic applied.