Download A relation is any set of ordered pairs

FST Chapter 2: Functions and Models (notes)
A relation is any set of ordered pairs. Often the second number in an ordered pair in
some manner depends on the first number. Because of this, the first variable in a relation
is called the independent variable and the second is called the dependent variable. Not
all relations are functions (but all functions are relations).

FUNCTION Def. 1: A function is a set of ordered pairs in which each first
element is paired with exactly one second element.
The list of first elements is the domain; the list of second elements is the range. The
domain consists of all allowable values of the independent variable; the range is the set of
all possible values of the dependent variable.

FUNCTION Def. 2: A function is a correspondence between two sets A and B in
which each element of A corresponds to exactly one element of B. Set A is the
domain; set B is the range.
The domain is (for our purposes) the set of all real numbers for which the function is
defined. (real numbers include the positive numbers, negative numbers and zero,
including fractions and decimals). A fraction is undefined when the denominator is 0.
L. Euler’s notation, or function notation: f(x) is read “f of x”, meaning the value of the
dependent variable when the independent variable is x.
Vertical Line Test: IN a function, only one value of the range is paired with each value
of the domain. A vertical line will only intersect the graph at one point.
Example : The cost of renting a car is $35 per day plus $.40/ mile
a. Which is true, “cost is a function of miles driven” or “miles driven is a function of
cost?”
b. Identify the independent and dependent variables.
c. Is this equation a function?
c. State the domain of the function (all possible independent values).
d. List 3 ordered pairs of the function.
e. complete the equation to express the relation between miles m and cost C:
C(m) = _______ + 35
FST Chapter 2: Functions and Models (notes)
Questions:
1. Determine whether the following graphs represent functions
2: The cost of renting a pool table at Johnny’s pool hall is a $10 flat fee plus $12
for each 30 minutes. There is a 4 hour limit per table.
a.
Is the cost the independent or dependent variable?
b.
write an equation that represents the cost (c) of renting a pool table
for (m) minutes.
c.
How much will is cost to rent a table for 90 minutes?
d.
What is the domain for the function in this situation?
e.
What is the range?
3. Find the range of the function with the rule: y  2x 2  10 (domain is all real numbers)