Functions vs Relations

Level 5 to Level 6
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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}.

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