Functions
2.1 Relations and Functions
Kudos
Know – How to identify functions. Know how to map
relations.
Know vocab…
Relation
Mapping Diagram
Domain
Function Notation
Range
Vertical Line Test
Control Variable
Dependent Variable
Understand what makes a relation a function.
Do- Be able to identify functions, graph relations, and
evaluate using function notation.
Control Variable
…is a variable that
determines or
controls another
variable.
Domain
The domain of a
function is all
possible values of the
control variable.
Dependent Variable
…is a variable that
is determined by or
depends on
another variable.
Range
The range of a
function is all
possible values of the
dependent variable.
To help you remember….
Dependent variable
Control variable
“_____ depends on ____”
•
•
•
•
•
•
Fastest walking speed : leg length
Definition : word
Radius: area of a circle
Person: birthday
Reciprocal : every real number (except 0)
Hours worked : salary earned.
“_____ depends on ____”
This
variable
goes on
the y-axis
This
variable
goes on
the x-axis
Which axis??
Hours worked
Salary
Which axis??
Area of a circle
Radius
Which axis??
Leg length
Walking speed
Which axis??
Every real
number (except 0)
Reciprocal
Relation
5
Ex1) Graph the coordinate points:
4
3
(–3, 3), (2, 2), (–2, –2),
(0, 4), (1, –2)
2
1
-5 -4 -3 -2 -1
1
2
3
4
-1
-2
-3
-4
-5
A relation is a set of pairs of input (x) and output (y) values.
Written: {(–3, 3), (2, 2), (–2, –2), (0, 4), (1, –2)}.
5
Relation
{(–3, 3), (2, 2), (–2, –2), (0, 4), (1, –2)}
Domain – the set of all inputs of a function (x-coordinates)
Domain: {-3, -2, 0, 1, 2 }
Range - the set of all outputs of a function (y-coordinates)
Range: { -2, 2, 3, 4 }
Relation
Ex2) Write the ordered pairs for the relation.
Find the domain and range.
Mapping Diagrams
Ex3) {(–3, 3), (2, 2), (–2, –2), (0, 4), (1, –2)}.
Domain
Range
Functions
A function is a relation in which each input value is paired
with only one output value.
Domain
Range
Domain
2
-2
-1
0
3
5
4
Function?
3
4
7
Function?
Range
5
6
8
Is it a
function?
Yes!
Remember
the vertical
line test?
Is it a
function?
No!
Remember the
vertical line
test?
Is it a
function?
No!
Is it a
function?
Yes!
Stop?
Notation for functions
•
•
•
•
y = f(x) say “f of x” (not f times x)
Control variable is the x
Dependent variable is the y
f(3) = 8 means the value of
f at 3 is 8
Use f(x) =
•Find f(4)
•Find f(-5)
•Find f(a)
2
x
Expand (x+3)2
2
•x
+ 3x +3x
2
•x + 6x + 9
2
+3
Expand
2
•x
2
(x+y)
+ xy +xy +
2
2
•x + 2xy + y
2
y
2
x
Use f(x) = + 2x
•Find f(3)
•Find f(-2)
•Find f(c + d)
Planner Time!
HW: 7, 12, 13, 17, 20, 21, 23, 25,
33, 37, 39, 41, 46, 47