# IB Maths Studies/Functions

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## Functions as a mapping[edit]

- relation - is a set of ordered pairs such as Q = {(2,3) (7,1) (8,3)}
- function - is a relation is which no two different ordered pairs have the same X coordination
- Domain - of a function is the set of independent values that are allowed
- Range - of a function is the set of all dependent values that are allowed.

X = Domain Y = Range

## Relation Properties[edit]

- Linear: y = mx + c; (Straight Line)
- Quadratic: y = ax^2 + bx + c; (Parabola)
- Polynomial: y = ax^3 + bx^2 + cx + d; (Cubic)
- Exponential: y = a * b^(k*x) + c; (Exponential)
- Reciprocal: y = (a / (x – b) + c; (Rectangular Hyperbola)
- Square Root: y = a √(x) + b; (Sideways Parabola)
- Reciprocal Squared y = (a / (x – b)^2) + c; (Truncus)
- Circular: r^2 = (x – a)^2 + (y - b); (Circle)