IB Maths Studies/Functions

Functions as a mapping

• 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

• 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)