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Chapter 1.2 Basics of Functions and Their Graphs
 What is relation?
A relation is any set of ordered pars.
 What is domain, range?
The set of all first components of the ordered pair is called the domain of the relation. And the set of all second components
is called the range of the relation.
Example: Find the domain and range of the relation:
{ (1,2) , (3, 4) , (6, 6)}
{ (apple, red), (banana, yellow) , (watermelon, green) }
 What is function?
A relation in which each member of the domain corresponds to exactly one member of the range is a function.
A function is a relation in which no two ordered pairs have the same first component and different second components.
Example: Are the following relation are function?
{ (1,1), (1,3)}
{ (9, 0) , (1,3) , (2,5) }
{ (apple, red) , (watermelon, green) , (apple, green) }
 What is domain, range (in function)?
A function is a correspondence from a first set, called the domain, to a second set, called the range, such that each element
in the domain corresponds to exactly one element in the range.
Example of function:
{ (0, 9.1), (10, 6.7), (20, 10.7), (30, 13.2), (36, 17.4)}
Example of Check point 2:
{ (1,2), (3,4) , (5, 6) , (5,8) }
{(1, 2), (3, 4), (6, 5), (8, 5)}
 Functions as Equations
**Function is usually in terms of equations rather than as sets of ordered pairs.
**If an equation is solved for y and more than one value of y can be obtained for a given x, then the equation does not define
y as a function of x.
 Inside of functions
Independent variable (the variable x is called the independent variable)
Dependent variable (the variable y is called the dependent variable)
Example: (Check point 3) Determine whether each equation defines y as a function of x :
a) 2x + y = 6 b) x2 + y2 = 1
 Function Notation
Function is often named by a letter such as , f, g, h, F, G, H. (Any letter can be used to name a function)
Input – x
Output – f(x) represent value of the function at the number x .
 Graph of Functions
All functions with equations of the form f(x) mx + b graph are straight line. Such functions, called Linear functions. (will be
discussed in detail in section 1.4).
 (optional) Vertical Line Test
Vertical line test can test out if a graph is a function or not.
If any vertical line intersects a graph in more than one point, the graph does not define y as a function of x.
 Identify domain and range from a function’s graph
Using Set – Builder Notation: {x | -2 < x < 2} (read as: the set of all x, such that -2 < x <2)
Using Interval Notation
: (-2, 2)
Domain: Set of inputs (Found on the x –axis)
Range : Set of outputs (Found on the y – axis)