Download Lesson 2-4 Definition of Function Student Copy

Precalculus Functions & Graphs
2.4 Definition of Functions
Notes
Mapping or Correspondence
1₵
Purple
25₵
Pink
$1
Red
50₵
Green
10₵
White
5₵
Blue
Domain
Domain - what goes in.
Range
Range - what comes out.
Precalculus Functions & Graphs
2.4 Definition of Functions
Notes
Mapping
1₵
25₵
$1
50₵
10₵
5₵
Domain
Purple
Pink
Red
Green
White
Blue
Range
Precalculus Functions & Graphs
2.4 Definition of Functions
Notes
Mapping
Do you think this mapping is fair?
Why or why not?
1₵
25₵
$1
50₵
10₵
5₵
Domain
Purple
Pink
Red
Green
White
Blue
Range
Precalculus Functions & Graphs
2.4 Definition of Functions
Notes
Mapping
Do you think this mapping is fair?
Why or why not?
1₵
25₵
$1
50₵
10₵
5₵
$2
Domain
Purple
Pink
Red
Green
White
Blue
Range
Precalculus Functions & Graphs
2.4 Definition of Functions
Notes
Mapping
1₵
25₵
$1
50₵
10₵
5₵
Domain
Do you think this mapping is fair?
Why or why not?
Yellow
Purple
Pink
Red
Green
White
Blue
Range
Precalculus Functions & Graphs
2.4 Definition of Functions
Notes
Function
Domain
Range
Precalculus Functions & Graphs
2.4 Definition of Functions
Notes
Terminology
f is increasing on
an interval I.
Definition
Graphical Interpretation
f  x1   f  x2 
whenever x1  x2
f(x2)
f(x1)
x1
f is decreasing
on an interval I.
f  x1   f  x2 
whenever x1  x2
f(x1)
x1
f is constant on
an interval I.
x2
f(x2)
x2
f  x1   f  x2 
for every x1 and x2
f(x1)
x1
f(x2)
x2
Precalculus Functions & Graphs
2.4 Definition of Functions
Example #1
If a and h are real numbers, find:
If f ( x)  x  6  2 x, find f (10), f ( 2), f ( 6)
Precalculus Functions & Graphs
2.4 Definition of Functions
You Try #1
If a and h are real numbers, find:
If f ( x)  2 x  3  4 x, find f (14)
This is not multiple choice just enter the answer.
Precalculus Functions & Graphs
2.4 Definition of Functions
You Try #2
If a and h are real numbers, find:
If f ( x)  2 x  3  4 x, find f (6).
This is not multiple choice just enter the answer.
Precalculus Functions & Graphs
2.4 Definition of Functions
You Try #3
If a and h are real numbers, find:
If f ( x)  2 x  3  4 x, find f (26).
This is not multiple choice just enter the answer.
Precalculus Functions & Graphs
2.4 Definition of Functions
Example #2
If a and h are real numbers, find:
f ( a  h)  f ( a )
f (a ), f (a ),  f (a ), f (a  h), f (a)  f (h),
,h  0
h
f ( x)  x 2  3 x  5
Precalculus Functions & Graphs
2.4 Definition of Functions
f ( x)  x 2  3 x  5
Example #2 Continued
If a and h are real numbers, find: f (a  h)  f (a ) , h  0
h
Precalculus Functions & Graphs
2.4 Definition of Functions
Example #3
If a is a positive real number, find:
g ( x)  3 x  2
1
1
g  ,
,g
 a  g (a)
 a ,
g (a)
Precalculus Functions & Graphs
2.4 Definition of Functions
You Try #4
If a is a positive real number, find:
g ( x)  5 x  4
1
1
g  ,
,g
 a  g (a)
Not a Quizdom Question
 a ,
g (a)
Precalculus Functions & Graphs
2.4 Definition of Functions
Example #4
Explain why the graph is or is not the graph of a function.
Precalculus Functions & Graphs
2.4 Definition of Functions
You Try #5
Is the graph the graph of a function, yes or no?
Precalculus Functions & Graphs
2.4 Definition of Functions
Example #5
Determine the domain D and the range R of the function?
Precalculus Functions & Graphs
2.4 Definition of Functions
You Try #6
Determine the domain D and the range R of the function?
Answer choices will appear after you have
had time to work the problem.
Precalculus Functions & Graphs
2.4 Definition of Functions
Example #6
Find the domain of f.
3x  4
f ( x)  2
x  6x  8
Precalculus Functions & Graphs
2.4 Definition of Functions
Example #7
Sketch the graph of f. Find the domain D and range R of f.
Find the intervals on which f is increasing, is decreasing, or
is constant.
f ( x)  x  3
Precalculus Functions & Graphs
2.4 Definition of Functions
You Try #7
Sketch the graph of f. Find the domain D and range R of f.
Find the intervals on which f is increasing, is decreasing, or
is constant.
f ( x)   x 2  2
Not a Quizdom Question