,1.1 Graphs and Graphing Utilities
Plotting Points in the Rectangular Coordinate System
Each point in the rectangular coordinate system corresponds to an ordered pair of real numbers ,
(x , g) .
The first number is the ✗ coordinate , which the distance and direction from the along the axis The second number the
shows
origin ✗ is
- -
.
which and direction from the
g- coordinate ,
shows the ver tical distance
origin along the
y-axis .
t =É¥
1-2,41 14 -21
Y
" , 4-
2-
.i¥
-
2- -2 -
-
4- -
4-
Graphs and Equations
A relationship between two
quantities can be expressed as an
equation in two variables, such as
y=4
A solution of an
equation with two variables ,
✗ and
y ,
is an ordered pair of real numbers with the following property
: when the ✗ -
coordinate is
substituted for ✗ and the g- coordinate is substituted for g in the equation ,
we obtain a true statement .
" ?%"""|°""""""
"" " "
?
"" "
" "" " =3
"
find the
y -1-3+11--2 1-3,2 )
-
we
2
y= 1-2+11=1 1-2,1 )
-
corresponding
,
1+11=0 C- 1,0 )
value of y
g- I
-
-
.
Intercepts
:¥÷¥→
An x -
intercept is the ✗ -
coordinate of a point where the
graph intersects the x-axis .
The
4•
Tnegraphcrossesthey-axisat lQ4J.Th
us, the g- intercept is 4
g- coordinate corresponding to an x intercept is always zero
-
.
A of is the intersects the
g- intercept a graph g- coordinate of a point where the
graph
The coordinate corresponding
g- axis . ✗ -
to a
g- intercept is always zero .
(-2,0).Thus,thex-inptis2☒
The graph crosses the x-axis at
@
, I. 2 Basics of Functions and their Graphs
Definition of a Function
A function is correspondence from first set called the domain , to second such that each element in the domain
a a ,
a set
,
called the
range ,
corresponds to
exactly one element in the range .
Function Notation
flx )
" "
The special notation ,
read f of ✗
"
or fat ✗
"
, represents the value of the function at the number ✗ .
Evaluating a Function
If f(× ) =
✗
2-
2×+7 ,
evaluate fl 5)-
ynegrapnoaafun.gionisgneg.am
f. (x ) -
-
✗ 2-2×+7 →
fl g) -
=L g) 2- 21
- -
g) + > Graphs of Functions :
g. g) = zg ,
,, , >
f(-5)= of its ordered pairs .
,,,,,a,n,µ * :# *
Vertical Line Test :
If intersects
any vertical line a graph
in more than 1 point, the graph does not
↳
n.am . µ. n.am .
A Relationship as a Function
A- relation in which each member of the domain corresponds to
exactly one member of the
range is a function .
Because ,
a function is a relation in
which no two ordered pairs have the same first component and different second components .
{ II. II. 11.21.12.3 ) } {11,1×21113,21}
D- I D- I
Not a Func .
Func .
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