(2-1) Relations and Functions

Cartesian Coordinate Plane Def: Composed of the x-axis (horizontal) and the y-axis (vertical) which meet at the origin (0,0).

Relation Def: Set of ordered pairs Example: {(3,2),(4,1),(7,3), (1,2),(6,3),(5,6)}

Quadrants Def: The Cartesian coordinate plane is divided into four quadrants (parts), which can be written in the form (x,y).

Domain Def: Domain of a relation is the set of all x-values in a set of ordered pairs.

Domain Def: Domain of a relation is the set of all x-values in a set of ordered pairs. x,y x,y x,y x,y x,y x,y Example: {(3,2),(4,1),(7,3),(1,2),(6,3),(5,6)}

Domain Def: Domain of a relation is the set of all x-values in a set of ordered pairs. x,y x,y x,y x,y x,y x,y Example: {(3,2),(4,1),(7,3),(1,2),(6,3),(5,6)} Domain: { 3, 4, 7, 1, 6, 5 }

Range Def: The range of a relations is the set of all y-values in a set of ordered pairs. x,y x,y x,y Example: {(3,2),(4,1),(7,3),(1,2),(6,3),(5,6)} Range: { 2, 1, 3, 2, 3, 6 } Range: { 2, 1, 3, 6}, you don’t repeat

Mapping Def: Shows how the member of the domain is paired with each member of the range X Y f(x) Example: {(3,2),(4,1),(7,3),(1,2),(6,3),(5,6)} x,y x,y x,y

Function Def: A function is a special type of relation in which each element of the domain is paired with exactly one element of the range X Y f(x) Example: {(2,4),(1,2),(5,4),(4,2)} x,y x,y

Not a Function XY f(x) Example: {(2,1),(4,3),(2,4),(1,1)} x,y x,y This is not a function because 2 goes to 1 and 3, which contradicts the definition of a function.

Discrete Vs. Continuous Discrete is a relation in which the Domain is a set of individual points. Continuous is when the domain of a relation has an infinite number of elements and the relation can be graphed with a line or smooth curve.

Independent Variable When an equation represents a function, the variable, usually x, whose values make up the domain is called the Independent Variable. y = 3x+4 Independent Variable

Dependent Variable The other variable, usually y, is called the Dependent Variable because its values depend on x. y = 3x+4 Independent Variable Dependent Variable

Vertical Line Test If no vertical line intersects a graph in more than one point, the graph represents a function.

Vertical Line Test If no vertical line intersects a graph in more than one point, the graph represents a function. Thus this is not a function because the vertical line crosses the graph through more than one point.

Evaluating a Function Given,find each value. (a) f (-3) Take original function Substitute Simplify = 9+2 =11

Evaluating a Function Given,find each value. (b) f (3z) Take original function Substitute Simplify

Class Work Determine whether each relation is a function. Write yes or no.

Discrete or Continuous Graph each relation or equation and find the domain and rang. Next determine if the relation is discrete or continuous. Then determine whether the relation or equation is a function.

Evaluate