Honors Precalculus Notes--Chapter 1, Functions and Graphs

,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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