# What is a function ?

function, in mathematics, **an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable)**. Functions are ubiquitous in mathematics and are essential for formulating physical relationships in the sciences.

describe the situation and the example of the function in everyday life.

**A car's efficiency in terms of miles per gallon of gasoline is a function. If a car typically gets 20 mpg, and if you input 10 gallons of gasoline, it will be able to travel roughly 200 miles.**

b) describe and explain how this knowledge helps people in their everyday life

It **helps us relate to others, work together, and give and receive instructions**. It helps us think about the past and plan for the future. Language enables us to communicate with others, to come up with and think through new ideas.

**Shadows**

The length of a shadow is a function of its height and the time of day. Shadows can be used to find the height of large objects such as trees or buildings; the same function rule (ratio) by which we compare the length of an upright ruler to its shadow will help us find the unknown input (the height of the large object) when we measure its shadow.