Transcript Algebra 2 - TeacherWeb

Algebra 2
3-8 Functions
3-8 Functions

WARMUP
Complete the table:
x
4 – 2x
(x, y)
-1
4 – 2(-1)
(-1, 6)
0
1
2
3
3-8 Functions
 A function is a correspondence between two
sets, D and R, that assigns to each member
of D exactly one member of R.
Real world example:
Post Office: The cost of mailing a letter is a
function of its weight – the heavier it is, the
more it will cost to mail. There is a
correspondence, cost to weight, given by a
definite rule.
3-8 Functions
 Another example.
Paul VI has a grade scale – a letter grade is a
function of the numeric grade earned by the
student. There is a correspondence, letter
grade to numeric grade, given by a definite
rule.
Can you think of any other examples?
3-8 Functions
 You can think of functions as a machine, that
you put something in, and get something out
on the other side, based on rules inside the
machine.
3-8 Functions

National Library of Virtual Manipulatives:
http://nlvm.usu.edu/en/nav/vlibrary.html
Check out the Function Machine…
Another cool one:
http://www.explorelearning.com/index.cfm?method=cRe
source.dspView&ResourceID=133
3-8 Functions
 Again, a function is a correspondence
between two sets, D and R, that assigns to
each member of D exactly one member of
R.
3-8 Functions
 Mapping diagrams in book…
3-8 Functions
 The set D is the domain of the function.
 The range of the function is the is the set of
all members of R assigned to at least one
member of D.
Note: Unless otherwise stated, domains and
ranges in our book will be sets of Real
numbers.
3-8 Functions
 So, an example of a rule for a function might
be:
“double the number.”
-2
-1
0
1
2
-4
-2
0
2
4
3-8 Functions
 The letters f, g, F, G, and occasionally ,
(Greek phi) are used to name functions.
In the book you might see arrow notation:
g: x
2x
This is read “g, the function that assigns to x the
number 2x”
3-8 Functions
 The graph of a function ƒ is the set of all
points (x, y) such that x is in the domain of ƒ
and the rule of the function assigns y to x.
 The values of a function are the members of
it’s range. If g: x
the value 4.
2x then g assigns to 2
 Functional notation: write g(x) = 4
3-8 Functions
 f(2) = 4, read “the value of f at 2 is 4” or
more commonly, “f of 2 is 4”
 In general:
f(x) denotes the value of f at x
BE CAREFUL: f(x) DOES NOT MEAN f
multiplied by x!!!
3-8 Functions
 Domains and ranges.
IMPORTANT:
 The domain of a function is the set of those
real numbers for which the equation
produces real numbers!
What are the domains of the following:
1
f ( x)  2
x 4
1
g(x)=
x( x  2)
h(x)= 2  x
3-8 Functions
 The range of functions are the values that
can come out of the function:
What are the ranges of the following
functions:
1
f ( x)  2
x 4
1
g(x)=
x( x  2)
h(x)= 2  x
3-8 Functions
 More practice…
 Homework