MA112 – 1.2 Functions and Graphs
Today:
 finish and collect group worksheet on
simple graphing
 2.1: concepts of domain, range, and
function
Announcements
 Homework 1.2 – part B assigned on
MyMathlab
 quiz Friday on finding domain
 Module 1 quiz next week – all material
covered
Naïve concept of function: plug in x, solve for y
x = input
y = output
(x,y) is an ordered pair
Example: f ( x)  5 x 3  10 , find f (0) , f (1) and f ( 2) .
f (0)  5  03  10  10  (0, 10) = (x,y)
f (1)  5 13  10  15  (1, 15) = (x,y)
f (2)  5  23  10  5  8  10  50  (2, 50) = (x,y)
More Advanced Graphing: Domain and Range
domain = all permitted values of x (values of x that can be plugged into the equation)
range = all values of y (values of y that result when you plug in any x)
Determining the Domain
The domain is either all the real numbers (domain=) or is restricted either by context or
by the impossibility of plugging in some values.
Restricted by context: Suppose that the cost of a box is a function of the length of the box.
We would only consider positive box sizes.
Impossible to plug in: There are exactly two reasons why it is impossible to plug in a
value of x:


you can’t take the square root of a negative number
you can’t divide by 0
example: (square root of a negative number)
y  x 1
(domain = x≥1)
You can also determine the domain and range from a graph.
Formal definition of a function
An equation is a function if every value in the domain maps to only one value in the
range.
You have exactly one output per input.
“You’re not allowed to have more than one answer per question.”
Identifying if something is a function
- whether a given correspondence is a function
- whether an equation is a function given its graph (vertical line test)
Whether a given correspondence is a function
Inputs/Outputs can be described with correspondences of arrows:
y  x2
Domain
Range

0
0

1
1

2
4

10
100

15
225
A correspondence (or relation) is a FUNCTION if and only if each element in the domain
maps to no more than one element in the range. (You’re not allowed to have more than
one output per input.)
Vertical line test: if the solution to an equation (i.e., the graph) ever has more than two
solutions for a single value of x, then it is not a function.
Is a function.
Not a function.