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Chapter 6: Problem 1

Explain what is meant by the term 'parameter'.

Short Answer

Expert verified
In summary, a parameter is a value or set of values that define, characterize, or influence a system within a specific context. Parameters can be found in multiple fields such as mathematics, e.g., variables in equations of curves, science, e.g., factors in an experiment, and technology, e.g., values passed to a function in programming. Understanding the concept of parameters is crucial in many disciplines as it enables us to manipulate and analyze systems effectively.

Step by step solution

01

Definition of Parameter

A parameter is a value or a set of values that define a given system or help in its identification and characterization. In mathematics, science, or technology, parameters are quantities that vary within a specific context and can be used to influence the behavior of a system or describe its properties.
02

Parameters in Mathematics

In mathematics, parameters can be variables that are commonly used to define a family of functions or curves. For example, in the equation of a straight line, y = mx + b, where 'm' denotes the slope of the line, and 'b' denotes the y-intercept, both 'm' and 'b' are parameters. They determine various characteristics of the line, such as its steepness and position, and can be adjusted to produce different lines.
03

Parameters in Science

In scientific experiments, parameters are any factors that can be varied, controlled, or measured. For example, in a study of plant growth, variables such as temperature, light exposure, and soil composition can be considered as parameters. By systematically changing these parameters, researchers can analyze the effects of each on the overall growth of the plant.
04

Parameters in Technology

In computer programming, parameters are values passed to a function or method, which then uses them to perform some calculation or operation. For instance, imagine a simple program that calculates the area of a rectangle. The function to compute the area might accept two parameters: the length and the width of the rectangle. In this case, the parameters are used to define the inputs to the function, and they help determine the output (the area). To sum up, the term "parameter" is essential in various fields, and it primarily refers to a value or set of values that help describe or influence the behavior or properties of a system.

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Most popular questions from this chapter

Explain what is meant by the 'argument' of a function.

By sketching a graph of \(y=3 x-1\) show that this is a one-to-one function.

Plot a graph of the following functions. In each case state the domain and the range of the function. (a) \(f(x)=3 x+2,-2 \leq x \leq 5\) (b) \(g(x)=x^{2}+4,-2 \leq x \leq 3\) (c) \(p(t)=2 t^{2}+8,-2 \leq t \leq 4\) (d) \(f(t)=6-t^{2}, 1 \leq t \leq 5\)

If \(f(x)=x+6\) and \(g(x)=x^{2}-5\) find (a) \(f(g(0))\), (b) \(g(f(0))\), (c) \(g(g(2))\), (d) \(f(g(7))\).

Explain what is meant by the inverse of a function.
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