Function properties and theirs grahps....

F U N C T I O N P R O P E R T I E S
10.4.1.3 - BE ABLE TO DETERMINE THE PROPERTIES OF A FUNCTION;
10.4.1.4 - BE ABLE TO DESCRIBE, ACCORDING TO A GIVEN GRAPH, THE FUNCTIONS OF ITS
PROPERTIES:
1) DOMAIN OF THE FUNCTION;
2) THE RANGE OF VALUES OF THE FUNCTION;
3) ZEROS OF THE FUNCTION;
4) THE FREQUENCY OF THE FUNCTION;
5) INTERVALS OF MONOTONICITY OF THE FUNCTION;
6) INTERVALS OF CONSTANT FUNCTION;
7) THE MAXIMUM AND MINIMUM VALUES OF THE FUNCTION;
8) EVEN, ODD FUNCTION;
9) LIMITED FUNCTION;
10) CONTINUITY OF FUNCTION;
11) EXTREMA OF THE FUNCTION;

T O D A Y Y O U W I L L B E A B L E T O :
1 ) D O M A I N O F T H E F U N C T I O N ;
2 ) T H E R A N G E O F V A L U E S O F T H E F U N C T I O N ;
3 ) Z E R O S O F T H E F U N C T I O N ;
4 ) T H E F R E Q U E N C Y O F T H E F U N C T I O N ;
5 ) I N T E R V A L S O F M O N O T O N I C I T Y O F T H E
F U N C T I O N ;
6 ) I N T E R V A L S O F C O N S T A N T F U N C T I O N ;
7 ) T H E M A X I M U M A N D M I N I M U M V A L U E S O F T H E
F U N C T I O N ;
8 ) E V E N , O D D F U N C T I O N ;
9 ) L I M I T E D F U N C T I O N ;
1 0 ) C O N T I N U I T Y O F F U N C T I O N ;
1 1 ) E X T R E M A O F T H E F U N C T I O N ; .

• Variables
These are the quantities in a function that
can change
• Dependent Variables
Depends on another quantity (y-values)
• Independent Variables
These quantities tend to have an affect on
the dependent variable. (x-values)

E X A M P L E
• Variables
Time and temperature
• Dependent Variables
Temperature (depends on the time of day)
• Independent Variables
Time (is unaffected by the temperature)
• Relating Variables
Often written as a ordered pair with the independent
variable first(time, temperature)

N O TAT I O N O F A F U N C T I O N
• In general we use x to represent the
independent variable and y to represent
the dependent variable.
• We write…
y = f(x) meaning y is a function of x
T = f(t) meaning Temperature is a function
of time

A F U N C T I O N B O X
• We put in an input (independent variable) apply a function and receive an
output (dependent variable).

D O M A I N A N D R A N G E
• The domain of a function is the set of all
possible inputs for the function. For example,
the domain of f(x)=x² is all real numbers, and
the domain of g(x)=1/x is all real numbers
except for x=0
• The range of a function refers to all the
possible values y could be.

Function properties and theirs grahps....

F I N D I N G D O M A I N A N D R A N G E F R O M
G R A P H S

W H A T A R E Z E R O S
O F A F U N C T I O N ?
The zeros of a function f(x) are
values of the variable x such
that the values satisfy the
equation f(x) = 0. The zeros of
a function are also called the
roots of a function. We can
find these zeros graphically as
well by determining the x-
intercepts of the graph.

I N T E R V A L S O F
M O N O T O N I C I T Y
O F T H E
F U N C T I O N , T H E
M A X I M U M A N D
M I N I M U M V A L U E S
O F T H E
F U N C T I O N ;

F R E Q U E N C Y A N D P E R I O D
• Frequency refers to the number of
times an event occurs in a given
period of time. In the context of
functions, it refers to the number of
times the graph of a function repeats
itself in a given amount of time
• The figure shows 4 periods of the
sine function in the interval [0, 2π].
Beginning at 0, the graph of sin(4x)
repeats every ….

D E T E R M I N I N G E V E N A N D O D D
F U N C T I O N S
• Some functions exhibit symmetry so that reflections result in the original graph. For
example, horizontally reflecting the toolkit functions f(x) = x 2
will result in the original
graph. We say that these types of graphs are symmetric about the y-axis. Functions
whose graphs are symmetric about the y-axis are called even functions.

C O N T I N U I T Y O F F U N C T I O N

Function properties and theirs grahps....

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