User:
• Matrices
• Algebra
• Geometry
• Funciones
• Trigonometry
• Coordinate geometry
• Combinatorics
 Suma y resta Producto por escalar Producto Inversa
 Monomials Polynomials Special products Equations Quadratic equations Radical expressions Systems of equations Sequences and series Inner product Exponential equations Matrices Determinants Inverse of a matrix Logarithmic equations Systems of 3 variables equations
 2-D Shapes Areas Pythagorean Theorem Distances
 Graphs Definition of slope Positive or negative slope Determine slope of a line Ecuación de una recta Equation of a line (from graph) Quadratic function Posición relativa de dos rectas Asymptotes Limits Distancias Continuity and discontinuities
 Sine Cosine Tangent Cosecant Secant Cotangent Trigonometric identities Law of cosines Law of sines
 Ecuación de una recta Posición relativa de dos rectas Distancias Angles in space Inner product

Graphs and Functions
Relations and Determinig Whether a relation is a Function

A relation is a set of ordered pairs.

There are several ways to write a relation:

You can list a set of ordered pairs:

{(8,-1), (9,-3), (10,-1), (13,5)}

You can draw a mapping diagram as shown below:

 The points in the mapping diagram are the same points that were listed in the set of ordered pairs. The first oval contains the x-values and the arrow points to the appropiate y-value.

You can also write a relation in a table:

 x y 8 -1 9 -3 10 -1 13 5

You can display a relation on a graph:

or finally you can write a relation as an equation: y = x2

A function is a relation where for every x there is exactly one value for y.

To classify relations as functions when you are given a list, a mapping diagram, or a table, check the x-values. If there are two x-values that are the same but have different y-values, then the relation is not a function. If all the x-values are different and have different y-values, then the relation is a fuction.

 This is a function! This is NOT a function!

To classify relations as functions when you are given a graph, you can use the Horizontal Line Test: If a vertical line intersects more than one point on the graph, then the relation is not a function. If a vertical line intersects the graph in only one point, then the relation is a function.

This is NOT a function!

To classify a relation as a function when you are given an equation, then graph the equation and look at the graph.