Chapter 1: Functions (Lesson A)

Section A: relations and Functions

Domain- the set of possible values on the horizontal axis. (x-axis)
Range- the set of possible values on the vertical axis. (y-axis)

Relations- any set of points pn the cartesian plane.
Equation- expresses the relation which connects the variable X and Y.

• y = x+3 (line equation), x = y^2 +1 (parabola)

These equations generate sets of ordered pairs.
             there are some relationships that can't be defined by an equation

Functions: a relation in which no two different ordered pairs have the same x-coordinate function is a special type of relation.

Testing for functions, algebric
             id a relation is given as an equation and the substitution of any value of x results in one, and only one, value of y, we have a function.
example-
y = x+3, let x equal any number.
x = 3, y = 3+3 =6 (correct/yes)

x = y^2+1 let x = 4.
x=4, 4 = y^2 +1 as we do the work we get negative square root of 3. (incorrect/no)

Geometric Test: vertical line test
         if we draw all possible vertical lines on the graph of a relation, the relation:
1. is a function if each line cuts the graph no more than once.
2. its not a function if the line cuts the graph more than once




Guess which graph passes the test.

Graphical Notes: if a graph contains a small open circle (end point), the endpoint is not included.
       if it contains a small filled in circle endpoint the endpoint is included.
       it it contains an arrow head at the end then the graph continue indefinitely in the general direction or the shape may repeat as it has done previously.