Function Rules: How To Describe Relationships Between Variables In Mathematics, Science, And Engineering.

Function Rule

An algebraic expression that defines a function.

A function rule is a mathematical expression that describes the relationship between the input (the independent variable) and the output (the dependent variable) of a function. It can also be referred to as a formula or equation that tells you what mathematical operation(s) to perform on the input value to get the output value. In other words, a function rule is a set of instructions that shows how to transform the input variable into the output variable.

For example, consider the function f(x) = 2x + 1. This function rule tells us that to find the output value (or f(x)) for any given input value (or x), we need to multiply the input by 2, and then add 1. So, if we plug in x = 3, we get:

f(3) = 2(3) + 1
f(3) = 6 + 1
f(3) = 7

Therefore, the output value (or f(x)) for an input value of 3 is 7, which follows the function rule f(x) = 2x + 1.

Function rules are essential in describing and predicting relationships between variables in many areas of mathematics, science, and engineering. They allow us to model and analyze real-life situations, and make predictions and decisions based on the data.

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