 # Functions vs Relations

Level 5 to Level 6 ##### Gotta-Otta Test

This diagnostic tool will help determine how ready you are for this lesson. It covers the topics you Gotta Know before starting this lesson and what you ‘Otta Know by the end of the lesson. If you score well on this test, skip to the next section.

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##### What is a relation?

A relation is a mathematical relationship between an independent/control variable and a dependent variable. We generally represent the independent variable with $x$ and the dependent variable with $y$. Relations can be modelled in many different ways.

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##### What is a function?

A function is a special type of relation in which every $x$ element produces ONE and ONLY ONE $y$ element. You can identify functions in a few different ways.

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##### Function Notation

Instead of using the letter $y$ to denote the dependent variable, we oftentimes use $f(x)$ pronounced “$f$ at $x$“. It represents where the function is at $x$.

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##### Basic Functions

Certain functions occur a lot in nature as many mathematical models follow patterns. We call these functions: basic functions and they include linear, quadratic, cubic, absolute value, radical and the reciprocal $\frac{1}{x}$.